We can use the equation for the angle of the bright fringes in a double-slit experiment. The answer is D. 15.1o.
where θ is the angle of the bright fringe, m is the order of the fringe (in this case, m=3), λ is the wavelength of the incident light, and d is the distance between the slits.
Plugging in the given values, we get:
sinθ = (3)(5.04x10^-7m)/(5.82x10^-5m) = 0.260
Taking the inverse sine of both sides, we get:
θ = sin^-1(0.260) = 15.1o
Therefore, the answer is D. 15.1o.
To find the angle of the 3rd order bright fringe, we can use the formula for the double-slit interference pattern:
mλ = d * sinθ
where m is the order number (3 in this case), λ is the wavelength of the incident light (5.04x10^-7 m), d is the distance between the slits (5.82x10^-5 m), and θ is the angle we want to find.
First, rearrange the formula to solve for the angle:
sinθ = (mλ) / d
Now, plug in the given values:
sinθ = (3 * 5.04x10^-7 m) / 5.82x10^-5 m
Calculate the result:
sinθ = 0.02594
Now, find the inverse sine (arcsin) of the result to get the angle:
θ = arcsin(0.02594) ≈ 1.49°
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how should a firm record an impairment in the value of property, plant, or equipment?
A firm should record an impairment in the value of property, plant, or equipment by reducing the carrying amount of the asset and recognizing the impairment loss as an expense in the financial statements.
When the value of property, plant, or equipment is impaired, meaning its recoverable amount is lower than its carrying amount, a firm should recognize this impairment in its financial statements. The impairment is recorded by reducing the carrying amount of the asset to its recoverable amount, which is the higher of its fair value less costs to sell or its value in use. The difference between the carrying amount and the recoverable amount is recognized as an impairment loss and recorded as an expense in the income statement. This adjustment reflects the decrease in the value of the asset and allows the firm to accurately report its financial position and performance.
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Which of the following is true
concerning the expression 6t+3+ t?
A 6t and 3 are like terms
B 6t and t are like terms
C The simplified form of the
expression is 6t+ 3.
D The simplified form of the
expression is 10t.
Answer:
the answer is B 6t and t are like terms
Calculate the length of ED and BE
WILL GIVE BRAINLIST TO BEST ANSWER
Find the value of x that makes lines u and v parallel
Answer:
x = 5
Step-by-step explanation:
12x + 5 = 65
subtract 5 from both sides
12x + 5 - 5 = 65 - 5
12x = 60
divide by 12
x = 5
Coressponding angles in parallel lines are equal and for u and v to be parallel,
So we have,
[tex]12x + 5 = 65[/tex]
[tex]12x = 65 - 5[/tex]
[tex]12x = 60[/tex]
[tex]x = \frac{60}{12} [/tex]
[tex]x = 5[/tex]
Hence the value of x must be 5° to make the lines u and v parallel
pls help Jiya is renting a truck to move into her college dorm. The rental company charges $55 for the first hour and then $10 per hour after that. If it will take Jiya 7 hours to move, which explicit formula describes how much it will cost her to rent the truck?
a.a7=55+(7+1)10
b.a7=10+(7-1)55
c.a7=10+(7-1)7
d.a7=55+(7-1)10
Use an Explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours .The correct answer is option (d) a7=55+(7-1)10
The rental company charges $55 for the first hour and then $10 per hour after that, we can use an explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours.
The explicit formula for the total cost of renting the truck for a given number of hours can be written as:
a(n) = c + (n-1)d
where a(n) is the total cost of renting the truck for n hours, c is the cost of the first hour, and d is the additional cost per hour.
Using this formula, we can find the cost of renting the truck for 7 hours:
a(7) = 55 + (7-1)*10
Simplifying the expression in the parentheses, we get:
a(7) = 55 + 6*10
Multiplying 6 by 10, we get:
a(7) = 55 + 60
Adding 55 and 60, we get:
a(7) = 115
Therefore, the explicit formula that describes how much it will cost Jiya to rent the truck for 7 hours is:
a7=55+(7-1)10
Simplifying the expression, we get:
a7 = 55 + 6*10
a7 = 55 + 60
a7 = 115
Therefore, the correct answer is option (d) a7=55+(7-1)10.
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a game is played by drawing one card at random from a standard 52-card deck. if the card is a diamond, the player wins. if the card is not a diamond, the player loses $52. in order for this to be a fair game, when the player wins, how much should they win?
To determine the fair amount the player should win, we need to calculate the probability of drawing a diamond from a standard 52-card deck. There are 13 diamonds in a deck, and 52 total cards, so the probability of drawing a diamond is 13/52, or 1/4. This means that there is a 25% chance of winning the game.
To make the game fair, the expected value of the game must be zero. The expected value is calculated by multiplying the amount won by the probability of winning, and subtracting the amount lost by the probability of losing. In this case, the amount lost is $52, and the probability of losing is 75%, or 3/4.
So, the expected value equation would be:
0 = (amount won)(1/4) - ($52)(3/4)
Solving for the amount won, we get:
Amount won = $208/1 = $208
Therefore, in order for this game to be fair, the player should win $208 when they draw a diamond. This makes the expected value of the game zero, ensuring that it is a fair game for both the player and the house.
Answer more than 100 words: To summarize, the amount the player should win in order for the game to be fair is $208. This calculation is based on the probability of drawing a diamond from a standard 52-card deck, which is 1/4 or 25%. By calculating the expected value of the game, we can determine the amount the player should win in order for the game to be fair. The expected value equation takes into account both the probability of winning and the amount lost when losing. By setting the expected value equal to zero and solving for the amount won, we can determine the fair amount the player should win. This ensures that the game is fair for both the player and the house, as the expected value is zero.
In a fair game, the expected value of the game should be zero, meaning the player neither wins nor loses money on average. To determine the winning amount, let's analyze the probabilities and outcomes of the game.
A standard 52-card deck has 13 diamonds and 39 non-diamond cards. The probability of drawing a diamond is 13/52 or 1/4, and the probability of drawing a non-diamond is 39/52 or 3/4. If the player loses, they lose $52.
Let X be the winning amount if the player draws a diamond. The expected value (EV) is given by:
EV = (probability of winning) * (winning amount) + (probability of losing) * (losing amount)
Since the game is fair, EV = 0. Therefore:
0 = (1/4) * X + (3/4) * (-52)
To solve for X, multiply both sides by 4:
0 = X - 3 * 52
Now, add 3 * 52 to both sides to find the winning amount:
X = 3 * 52
X = $156
In order for this game to be fair, the player should win $156 when they draw a diamond.
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the weights of people in a certain population are normally distributed with a mean of 154 lbs and a standard deviation of 23 lbs. what is the distribution of the mean of random samples of size 4?
Answer:
Step-by-step explanation:
The distribution of the mean of random samples of size 4 can be approximated by a normal distribution with a mean of 154 Ibs (same as the population means) and a standard deviation of 11.5 Ibs (which is the population standard deviation divided by the square root of the sample size, i.e. 23 Ibs/ sqrt (4)= 11.5 Ibs). This is known as the Central Limit Theorem.
there were 375 books sold last week at Sid's Bookstore. The table below summarizes these books by genre. This information is also presented as a circle graph.
Find the central angle measure, x° for the Self-Help slice in the circle graph. Do not round.
The central angle formed by the Self Help slice is 86.4°.
A circle is formed when you draw a point and connect it from end to end forming a complete revolution.
We have to find the central angle formed by the Self Help slice
One revolution equals 360°.
Therefore, each piece of pie for each type of book is a fraction of one revolution.
The fraction can be determined by dividing the number for a specific type of book to the total number of books.
Specifically, the fraction for the Self Help slice would be 90/375 which is equal to 0.24 or 24%.
Then, 24% of 360 is 86.4.
Therefore, the central angle formed by the Self Help slice is 86.4°.
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There are 375 books sold at Sid's Bookstore. The table below summarizes these books by genre. This info is presented in circle graph. Find the central angle measure for Self Help slice in graph. Mystery 99, romance 81, self help 90, cooking 57, biography 48.
PLS HELP IM TIMED TY
Solve the equation. Enter your answer as an equation that shows the value of
the variable (like s= 2/3, or 4= w).
-7x-3=-31
The solution to the equation -7x - 3 = -31 is x = 4.
To solve the equation -7x - 3 = -31, we will isolate the variable x.
Step 1: Begin by moving the constant term to the other side of the equation.
-7x - 3 + 3 = -31 + 3
Simplifying, we get:
-7x = -28
Divide both sides of the equation by -7 to solve for x.
(-7x) / -7 = (-28) / -7
Simplifying, we have:
x = 4
Therefore, the solution to the equation -7x - 3 = -31 is x = 4.
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What is the answer to this question pls helppp 1/4 0f 68
Answer:
87
Step-by-step explanation:
beause
PLEASE HELP ME!!! THIS IS TIMED!! BRAINLIEST & 15 POINTS
Answer: I think the answer is A
Step-by-step explanation:
g a biker is riding along a trail at 13ft/s . she spots an aspen tree that is 15 feet away from a traffic cone located along the trail at the shortest distance from the trail to the aspen tree (see diagram). how fast is the angle between her line of sight and the trail changing when she is 25 feet away from the tree?
Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.
To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:
tan(θ) = x/15
We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:
d^2 = x^2 + 25^2
Taking the derivative of both sides with respect to time t, we get:
2d (dd/dt) = 2x (dx/dt)
Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):
tan(θ) = x/15
sec^2(θ) (dθ/dt) = (1/15) (dx/dt)
(dθ/dt) = (1/15) (dx/dt) sec^2(θ)
We can use the equation for d to solve for x:
x^2 = d^2 - 25^2
2x (dx/dt) = 2d (dd/dt)
(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)
(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)
Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):
(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))
(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))
(dθ/dt) = (13/375) sec^2(arctan(15/25))
(dθ/dt) ≈ 0.039 radians per second
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Find the distance between the points A and B given below.
(That is, find the length of the segment connecting A and B.)
Round your answer to the nearest hundredth.
Answer:
Measure the distance between those 2 points, A and B. Then when you get your answer, round it to the second number after your decimal. (The hundredth place) It is explained more below:
Step-by-step explanation:
After measuring, you should get a decimal number. With that number, you need to round to the nearest hundredth.
-Meaning you need to check the 2nd number right after the decimal. The second number right after the decimal will be 2 in this example.
If the number after 2 is less than five, you can just remove all the numbers after 2, leaving everything else the same. If the number after 2 is more than five or is exactly 5, you would change 2 to one number higher. (In this example, you would make it 3) Then you can remove all numbers after the 2 (which turned into 3 now)I hope this helped. <3
please help fast with my assignment
if 63 adults represent 87.5% of the people who visited a museum over a noon hour,
how many people visited the museum during the noon hour
A.72
B.86
C.135
D.151
Answer:
A. 72
Step-by-step explanation:
63/x = 87.5/100
x = 6300 divided by 87.5
x = 72
Write the three to five sentences explaining the importance of learning statistics in your life as a student
Learning statistics is essential for students as it helps them make sense of data and draw meaningful conclusions. It enables students to understand and analyze complex data, make informed decisions, and solve real-world problems.
Explanation:
Statistics is used in many fields of study, including business, economics, psychology, and social sciences. As a student, learning statistics can help you make sense of the vast amounts of data you encounter, whether it's in research papers, surveys, or experiments. Statistics enables you to analyze and interpret data, identify trends and patterns, and draw meaningful conclusions.
This can be useful in making informed decisions, solving problems, and developing new theories. Moreover, knowledge of statistics can also be valuable in your future career, as many professions require an understanding of data analysis and statistical methods. In short, learning statistics is an essential skill that can help you succeed academically and professionally.
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if you always test whether the number is positive or negative, big endian is more easy to use than little endian. true false
the statement "if you always test whether the number is positive or negative, big endian is more easy to use than little endian" is incorrect.
Endianness refers to the way in which a computer stores data in memory. In big endian, the most significant byte is stored at the smallest address and the least significant byte is stored at the largest address. In little endian, the least significant byte is stored at the smallest address and the most significant byte is stored at the largest address.
The choice between big endian and little endian has no impact on testing whether a number is positive or negative. Both endianness formats can store positive and negative numbers in the same way.
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Helppppppppp pleaseeeeee
The amount of wrapping paper that is needed to cover the package is 1625 sq cm.
How to determine the amount of wrapping paperTo determine the amount of wrapping paper that is required to cover the package, we will be determining the surface area of a triangle with the formula: A = 1/2 × b × h.
To find this surface area, we will go around the triangle while considering the bases and heights as follows:
((20 + 5) * 5 /2) * 2 + (20 * 30) + (17 * 30) + (5 * 30) + (8 * 30)
125 + 600 + 510 + 150 + 240
1625 sq cm
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If all are equally likely, find the number of possible outcomes
4 play dates, 3 show times
There are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.
For each play date, you have 3 options for the show time.
Since the events are independent and all options are equally likely, you can multiply the number of options together to find the total number of possible outcomes.
Number of possible outcomes
= Number of play dates × Number of show times
= 4 × 3
= 12
Therefore, there are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.
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ANSWER BY THE CHOICE IN THE BOTTOM NOT BY WHAT YOU WANT please answer correctly an quick
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
The mean distance thrown is approximately 37.31 feet. the Average distance thrown by the heavy ball.
To find the mean of the distances thrown from the stem-and-leaf plot, we need to add up all the distances and divide by the total number of throws.
From the stem-and-leaf plot, we can see that there are 13 throws in total.
To add up the distances, we can use the key to interpret the plot: for example, the number "31" means that one throw went 3.1 feet. Using this method, we can find the following distances:
20, 22, 25, 31, 33, 34, 41, 41, 45, 50, 56, 67, 71
Adding up these distances, we get a total of 485.
To find the mean, we divide by the total number of throws:
mean = 485/13 ≈ 37.31
Therefore, the mean distance thrown is approximately 37.31 feet. the average distance thrown by the heavy ball.
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After heating up in a teapot, a cup of hot water is poured at a temperature of 203∘ F. The cup sits to cool in a room at a temperature of 69∘F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
T=Ta+(T0-Ta)e^-kt
Ta = the temperature surrounding the object
T0 = the initial temperature of the object
t= the time in minutes
T= the temperature of the object after t minutes
k= decay constant
The cup of water reaches the temperature of 185∘F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
Enter only the final temperature into the input box.
The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:
155ºF.
How to obtain the temperature?The temperature function is defined as follows:
[tex]T(t) = T_a + (T_0 - T_a)e^{-kt}[/tex]
Considering the surrounding and initial temperature, we have that the function is given as follows:
[tex]T(t) = 69 + 135e^{-kt}[/tex]
The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:
[tex]185 = 69 + 135e^{-1.5k}[/tex]
[tex]e^{-1.5k} = \frac{116}{135}[/tex]
[tex]k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}[/tex]
k = 0.1011.
Hence:
[tex]T(t) = 69 + 135e^{-0.1011t}[/tex]
Hence the temperature after 4.5 minutes is given as follows:
[tex]T(4.5) = 69 + 135e^{-0.1011 \times 4.5}[/tex]
T(4.5) = 155ºF.
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Need Help ASAP! Please
2. Given the regular polygon below, what is the measure of each measured angle? *
12
Om<1 = 72; m>2 =
108
m<1 = 36; m>2 = 72
Om<1 = 72; m>2 = 54
Om<1=36; m>2 = 144
The measure of the angles m∠1 and m∠2 for the polygon are 72° and 54° respectively.
How to calculate for the interior angles of a polygonTo calculate the sum of interior angles of a polygon, you can use the following formula:
Sum of interior angles = (n-2) x 180 degrees
Where "n" represents the number of sides (or vertices) of the polygon.
Given the 5 sided polygon;
(5 - 2) × 180 = 540
one interior angle = 540/5 = 108°
m∠2 = 108°/2
m∠2 = 54°
m∠1 = 180 - [2(54°)]
m∠1 = 180 - 108
m∠1 = 72°
Therefore, the measure of the angles m∠1 and m∠2 are 72° for the polygon and 54° respectively.
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Pls help, thankssssss
30 points
Answer:option c is the answer
Step-by-step explanation:
What equation is equivalent to 3x - 12 = -9
The equation which is equivalent to 3x - 12 = -9 is 3(x - 4) { -9
What equation is equivalent?3x - 12 = -9
The equation is divided into two parts; right part and left part
From the left part; find the common factor of 3x and 12 which is 3
So,
3(x - 4) = -9
3x - 12 = -9
Add 12 to both sides
3x = -9 + 12
3x = 3
divide both sides by 3
x = 3/3
x = 1
Hence, the value of x based on the given equation is 2
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Writing unit fractions with a common denominator to add or subtract
finding 1/4-1/2 pls help
1/4 - 1/2 = -1/4. Don't forget to include the negative sign in your answer, which indicates that the result is less than 0. it's important to find a common denominator so that you can add or subtract them easily.
To subtract unit fractions like 1/4 and 1/2, you need to find a common denominator. A common denominator is a number that both denominators can divide into evenly. In this case, the smallest common denominator is 4, since 4 can be divided evenly by both 4 and 2.
To get both fractions to have a denominator of 4, you need to multiply 1/4 by 1 and 1/2 by 2/2, which equals 2/4.
Now that both fractions have the same denominator, you can subtract the numerators:
1/4 - 2/4 = -1/4
Overall, when working with unit fractions,
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a hotel near the university always fills up on the evening before football games history has shown that when the hotel is fully booked, the number of last minute cancellations has a mean of five and a standard deviation of three. the average room rate is $80. when the hotel is overbooked, the policy is to find a room in a nearby hotel and to pay for the room for the customer. this is usually costs the hotel approximately $200 since rooms booked on such late notice or expensive. how many rooms should the hotel overbooked?
The hotel should overbook enough rooms to maximize revenue without incurring expensive costs due to last-minute cancellations. To determine the optimal number of rooms to overbook, consider the following:
1. The average number of cancellations is 5 with a standard deviation of 3.
2. The average room rate is $80.
3. The cost of accommodating overbooked customers in a nearby hotel is $200.
Using these figures, the hotel can calculate the expected revenue for each room overbooked, while considering the risk of cancellations. The best approach is to use a probabilistic model, such as the normal distribution, to estimate the optimal number of rooms to overbook based on these statistics.
A detailed analysis would require further calculations and simulations, which are beyond the scope of this answer. However, a basic guideline for the hotel would be to overbook only a few rooms (e.g., 1-3) to minimize the risk of incurring the high cost of accommodating customers in nearby hotels while still maximizing the revenue from potential cancellations.
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if a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at least 4 fives?
To find the probability of getting at least 4 fives, we sum up the probabilities of these two cases:
P(at least 4 fives) = P(4 fives and 1 non-five) + P(5 fives)
To calculate the probability of getting at least 4 fives when rolling a fair die 5 times, we need to consider the different possible outcomes.
The probability of rolling a five on a fair die is 1/6, and the probability of not rolling a five is 5/6.
To determine the probability of getting exactly 4 fives and 1 non-five, we use the binomial probability formula:
P(4 fives and 1 non-five) = (5 choose 4) * (1/6)^4 * (5/6)^1
Similarly, for getting exactly 5 fives, we have:
P(5 fives) = (5 choose 5) * (1/6)^5 * (5/6)^0
Rounding the result to the nearest thousandth, we get the probability of getting at least 4 fives when rolling a fair die 5 times.
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In a random sample of 144 observations, P = 0.6. The 95% confidence interval for P is 0.52 to 0.68 0.144 to 0.200 0.60 to 0.70 0.50 to 0.70
The correct answer is: In a random sample of 144 observations, with a sample proportion of 0.6, the 95% confidence interval for the true population proportion is estimated to be between 0.52 and 0.68.
This means that if we were to repeat this sampling process many times and construct a confidence interval each time, we would expect 95% of those intervals to contain the true population proportion. The other options given are not correct as they do not accurately reflect the information given in the question.
In a random sample of 144 observations, with P = 0.6, the 95% confidence interval for P can be calculated using the following steps:
1. Identify the sample proportion (p) and the sample size (n): p = 0.6 and n = 144.
2. Calculate the standard error (SE) of the sample proportion using the formula: SE = sqrt[(p * (1 - p))/n]. In this case, SE = sqrt[(0.6 * (1 - 0.6))/144] = sqrt[(0.6 * 0.4)/144] = sqrt[0.24/144] = 0.04.
3. Find the critical value (z) for the 95% confidence interval using a z-table or a calculator. For a 95% confidence interval, the critical value is approximately 1.96.
4. Calculate the margin of error (ME) using the formula: ME = z * SE. In this case, ME = 1.96 * 0.04 = 0.0784.
5. Determine the lower and upper bounds of the 95% confidence interval by adding and subtracting the margin of error from the sample proportion: Lower Bound = p - ME = 0.6 - 0.0784 = 0.5216; Upper Bound = p + ME = 0.6 + 0.0784 = 0.6784.
So, the 95% confidence interval for P is approximately 0.52 to 0.68.
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the ratio of children to adults on a school trip is initially 10:1 this does not meet government regulations, so 5 more children and 5 more adults join the trip so that the ratio is now 9:1 how many children are there now
The number of children are there in the given scenario are 400.
Given that, the ratio of children to adults on a school trip is initially 10:1.
Here, the given ratio can be written as 10x:1x
5 more children and 5 more adults join the trip so that the ratio is now 9:1
10x+5:1x+5
The new ratio is (10x+5)/(x+5) = 9/1
10x+5=9(x+5)
10x+5=9x+45
10x-9x=45-5
x=40
So, the number of children =10x=400
Therefore, the number of children are there in the given scenario are 400.
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How do I solve this?
The trigonometric identity 1 + cot⁴θ = cosec⁴θ - 2cot²θ
What are trigonometric identities?Trigonometric identities are mathematical equations that contain trigonometric ratios in which one side is equal to the other.
Given the trigonometric identity
1 + cot⁴θ = cosec⁴θ - 2cot²θ, we need to show that the Left hand side L.H.S equals the Right Hand side R.H.S. we proceed as follows.
So, L.H.S = 1 + cot⁴θ
Now using the trigonometric identity
1 + cot²θ = cosec²θ
Making cot²θ subject of the formula, we have that
cot²θ = cosec²θ - 1
So, substituting this into the equation, we have that
1 + cot⁴θ = 1 + (cot²θ)²
= 1 + (cosec²θ - 1)²
Expanding the bracket, we have that
= 1 + cosec⁴θ - 2cosec²θ + 1
= cosec⁴θ - 2cosec²θ + 1 + 1
= cosec⁴θ - 2cosec²θ + 2
= cosec⁴θ + 2 - 2cosec²θ
= cosec⁴θ + 2(1 - cosec²θ)
= cosec⁴θ + 2cot²θ
= R.H.S
Since L.H.S = R.H.S
1 + cot⁴θ = cosec⁴θ - 2cot²θ
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