Sin2A+Sin2B÷Sin2A-Sin2B=Tan(A+B)÷Tan(A-B) Prove that​

Answers

Answer 1

Take L.H.S sin2A+sin2B/sin2A-sin2B

= sin2A+sin2B/sin2A-sin2B

Put

[sinC+sinD = 2sin(C+D)/2cos(C-D)/2]

[sinC-sinD = 2cos(C+D)/2.sin(C-D)/2]

= 2 sin(2A+2B)/2 cos(2A-2B)/2 / 2 cos(2A+2B) sin(2A-2B)

= sin(A+B).cos(A-B)/cos(A+B).sin(A-B)

= sin(A+B)/cos(A+B) . cos(A-B)/sin(A-B)

= tan(A+B).cot(A-B)

= tan(A+B).1/tan(A-B)

= tan(A+B)/tan(A-B)

∴ Hence we proved sin2A+sin2B/sin2A-sin2B=tan(A+B)/tan(A-B)


Related Questions

A duck has 1,100 feathers. It went for a swim in a pond and lost 2/100 of its feathers. How many feathers did it lose?

Answers

Answer:

It lost 22 feathers.

Step-by-step explanation:

To complete this problem, this expression will be used: 2x/100.

2(1100)/100 {Multiply 2 by 1100}

2200/100 {Simplify by cancelling out 100}

22/1 {Divide}

22 feathers were lost.

Add .003, 265.8, 83.04
and 1972

Answers

Answer: 2.320.843

Explanation: Calculator

(B) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is normal with μ (mean) = 15.5 and σ (standard deviation) = 3.6. What is the probability that during a given week the airline will lose between 11 and 19 suitcases?

Answers

Answer:

The correct answer is "0.7289".

Step-by-step explanation:

The given values are:

Mean,

[tex]\mu = 15.5[/tex]

Standard deviation,

[tex]\sigma = 3.6[/tex]

As we know,

⇒ [tex]z = \frac{(x - \mu)}{\sigma}[/tex]

The probability will be:

⇒ [tex]P(11< x< 19) = P(\frac{11-15.5}{3.6} <z<\frac{19-15.5}{3.6})[/tex]

                             [tex]=P(z< 0.9722)-P(z< -1.25)[/tex]

By using the z table, we get

                             [tex]=0.8345-0.1056[/tex]

                             [tex]=0.7289[/tex]

a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold​

Answers

Answer:

325 pencils, 650 markers, 975 pens

Step-by-step explanation:

in picture.

A company that makes mobile applications surveyed every 10th customer to learn more about how often customers are using one of the company’s new apps. The table shows the results of the survey.

Feedback Number
use frequently
51
use sparingly
23
do not use
12

What is the predicted percentage of customers who use the new app either frequently or sparingly?

A.
59%
B.
74%
C.
85%
D.
86%

Answers

The answer is D 86%

Answer:

I hope this helps

Step-by-step explanation:

write your answer as an integer or as a decimal rounded to the nearest tenth.​

Answers

Answer:

6.43

Step-by-step explanation:

Cosine: cos(θ) = Adjacent / Hypotenuse

cosine of 39 degrees = 5/x

.77714596145 = 5/x

x = 5/.77714596145

x= 6.43379782952

The humidity is currently 56% and falling at a rate of 4 percentage points per hour. (a) Estimate the change in humidity over the next 20 minutes. (Round your answer to one decimal place.) -1.4 Incorrect: Your answer is incorrect. percentage points

Answers

Answer:

The change is of -1.3 percentage points.

Step-by-step explanation:

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

This means that after n hours the humidity is of:

[tex]H(n) = 56 - 4n[/tex]

Estimate the change in humidity over the next 20 minutes.

It currently is 56%.

20 minutes is 20/60 = 1/3 of an hours, so:

[tex]H(\frac{1}{3}) = 56 - 4\frac{1}{3} = 54.7[/tex]

Change:

54.7 - 56 = -1.3

The change is of -1.3 percentage points.

The change in humidity over the next 20 minutes falling at a rate of  4 percentage points per hour is -1.3.

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

What is the formula used to determine the change in humidity?

The change is determined by the small about of humidity changes x to x+h, so the output of x+h is the value of f at x plus the approximate change in f, that is

[tex]\rm f(x+h) =f(x) + f'(x) \times h[/tex]

f(x)= 56%

20 minutes is 20/60 = 1/3 of an hours

So, The change in humidity is

[tex]f'(x) = 4 \times 1/3[/tex]

f'(x) = 1.3

Here, it is falling at the rate of 4% point per hour so we will take it as negative as -1.3.

Learn more about changes in humidity;

https://brainly.com/question/14363655

2^17+2^14 chia hết cho 9

Answers

Step-by-step explanation:

không khó lắm đâu ._.._.._.

find the quadratic equations whose roots are 3 and -4

Answers

Answer:

Hello,

Step-by-step explanation:

(x-3)*(x+4)=0 or x²+x-12=0

Answer:

Step-by-step explanation:

[tex]\displyastyle \Large \boldsymbol{} (x-x_1)(x-x_2) \ \ x_1 \ ; \ x_2 -roots \\\\(x-3)(x-(-4))=(x-3)(x+4)=\boxed{x^2+x-12}[/tex]

∫dx/(x+√(x^{2} +x+1)

Answers

Answer:

es1433

Step-by-step explanation:

Write an equation that has the zero's x={−1,−6}

Answers

Answer:

Step-by-step explanation:

If a zero is x = -1, then the factor, going one step backwards, is (x + 1) = 0; if the other zero is x = -6, then the factor is (x + 6) = 0. Now, going backwards one step further, we FOIL those out:

(x + 1)(x + 6) to get x-squared + 6x + 1x + 6 which combines to

[tex]x^2+7x+6=y[/tex]

FOILing those factors together is the opposite of factoring. Factoring gets you the factors, while FOILing puts them back together in the original equation.

1. A helicopter is at a position from two VORS (VHF Omnidirectional
Radio Range, an aircraft navigation system operating in the VHF band -
not covered in chapter) as in the diagram shown below. Given the angles
shown, find the third angle.
Helicopter
74.0°
66.0°
VOR
VOR

Answers

The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees

The diagram is not shown; however, the question can still be answered.

The given angles are:

[tex]\theta_1 = 74.0^o[/tex]

[tex]\theta_2 = 66.0^o[/tex]

Represent the third angle as [tex]\theta_3[/tex]

The helicopter and the 2 VORs form a triangle.

So, we make use of the following theorem to calculate the third angle

[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle

Substitute known values

[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]

[tex]140.0^o + \theta_3= 180^o[/tex]

Collect like terms

[tex]\theta_3= 180 -140.0^o[/tex]

[tex]\theta_3= 40^o[/tex]

Hence, the third angle is 40 degrees.

Learn more about angles in a triangle at:

https://brainly.com/question/14780489

if x+y=2 and x=4 then x+2y​

Answers

I’m sure the answer is just 4?
If x+y=2 and x=4, then to make that statement true, y has to equal -2.
So x+2y= 4+2-2= 4

HELP ASAP! Can someone please help me with this problem. I tried inputting the numbers to find the mean but I did not get the right answer. Can someone please help me with the last box? Thank you for your time!

Answers

Answer:

try 17.6

Step-by-step explanation:

for the mean you have to add all the numbers then divide the sum by the total number of numbers you added

Try 1.77181 and try rounding it to different decimal points

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis.

Answers

Using the shell method, the volume integral would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]

That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].

The volume itself would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]

Using the disk method, the integral for volume would be

[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]

where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.

The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

What is integration?

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

[tex]\rm y = x^8[/tex]   or

[tex]x = \sqrt[8]{y}[/tex]

And  y = 256

By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.

[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]

Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]

[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]

After solving definite integration, we will get:

[tex]\rm V = \pi(\frac{4096}{5} )[/tex]  or

[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit

Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

Learn more about integration here:

brainly.com/question/18125359

on a recent algebra test the highest grade was 36 points more then the lowest grade. the sum of the two grades was 132. find the lowest grade.

Answers

So what you need to do is find x in this equation: 2x+36=132. We get x=48. The lowest score was 48 points and the highest (Just in case you need it) is 84 points. Hope this helps.

ANSWER NOW IM TIMED Louie uses 10 feet of wood, 16 wheels and one can of paint for every 4 skateboards he builds.


A 4-column table with 3 rows. Column 1 is labeled Skateboards with entries 1, 4, 10. Column 2 is labeled Wood with entries blank, 10 feet, blank. Column 3 is labeled Wheels with entries blank, 16, blank. Column 4 is labeled paint with entries blank, 1 can, blank.


Use the table to find how much of each item Louie needs to build 10 skateboards.


Louie needs



feet of wood,


wheels, and


cans of paint.

Answers

Answer: 25 feet of wood

40 wheels and 2.5 cans of paints

Step-by-step explanation:

Answer:

25 feet of wood

40 wheels and

2.5 cans of paints

Step-by-step explanation: I did this before Also can i get brainlyist please

Select the correct answer.
Given the following formula, solve for l.



A.

B.

C.

D.

Answers

Please rewrite the question or add a picture for it

Answer:

c

Step-by-step explanation:

took the test so i assume its this question

Find the answer for x and y

Answers

Answer:

x = 57

y = 57

Step-by-step explanation:

because of the two parallel lines :

41+y+8+74 = 180 add like terms

y + 123 = 180 subtract 123 from both sides

y = 57

x - 3 + 41 + y + 8 = 180 because they make a straight line

x + y + 46 = 180

x + 57 + 46 = 180

x + 123 = 180 subtract 123 from both sides

x = 57

Which phrase describes an unknown or changeable quality?
3 feet and 7 inches
4 quarts in a gallon
2 o'clock in the afternoon
The height of the building times 1/2

Answers

Answer:

it should be the height of the building time 1/2

Step-by-step explanation:

let me know if its correct or incorrect we'll I hope this help you

You need a 75% alcohol solution. On hand, you have a 60 mL of a 55% alcohol mixture. You also have 85% alcohol mixture. How much of the 85% mixture will you need to add to obtain the desired solution?

You will need_____ mL of the 85% solution

Answers

60 mL=55% alcohol

?mL=85% alcohol

85×60÷55

=92.727 mL

I think do like this....I'm not sure

Hope this help you

9514 1404 393

Answer:

  120 mL

Step-by-step explanation:

Let x represent the amount of 85% solution needed. Then the total amount of alcohol in the mix is ...

  0.55(60) +0.85(x) = 0.75(60 +x)

  33 + 0.85x = 45 +0.75x . . . . . . . eliminate parentheses

  0.85x = 12 +0.75x . . . . . . . . . .subtract 33

  0.10x = 12 . . . . . . . . . . . . . . subtract 0.75x

  x = 120 . . . . . . . . . . . . . . multiply by 10

You will need 120 mL of the 85% solution.

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 2323 Pennies 55 Dimes 2020 Nickels 1919 Quarters Copy Data What is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel

Answers

Answer:

The answer is "0.081"

Step-by-step explanation:

Dimes [tex]= 55[/tex]

Calculating total coins [tex]= (23+55+20+19) = 117[/tex]

P(for a dime) [tex]= \frac{55}{117}[/tex]

Calculating remaining coins [tex]= 116[/tex]

Nickels [tex]= 20[/tex]

P(for nickel draw in second) [tex]= \frac{20}{116}[/tex]

P(for a dime after that a nickel, without replacement)

[tex]= \frac{55}{117} \times \frac{20}{116} \\\\= \frac{1100}{13572} \\\\=0.081[/tex]

The graph below displays a fire department’s response time, which measures the time from when the alarm is sounded at the firehouse to the time the first fire engine leaves the station.

A histogram titled Fire Department Response Times has response time (seconds) on the x-axis and relative frequency on the y-axis. 20 to 30, 0.07; 30 to 40, 0.08; 40 to 50, 0.2; 50 to 60, 0.32; 60 to 70, 0.18; 70 to 80, 0.13; 80 to 90, 0.04.

Which interval accounts for the lowest percentage of response times?

20–30 seconds
30–40 seconds
70–80 seconds
80–90 seconds

I think its (D), 80-90 seconds. Someone check me.

Answers

Answer:

I also think this is D.

Step-by-step explanation:

This question isn't asking for a lot of math so.

According to the graph, the 80-90 seconds response times are the shortest, meaning it is the least frequent or common.

Plus, it would be a bad thing if it was average anyways, and is outlined by the histogram.

A simple random sample of 41 men from a normally distributed population results in a standard deviation of 10.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts​(a) through​ (d) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic; χ2 = ___ ​(Round to three decimal places as​ needed.)
c. Find the​ P-value; ​P-value = ____ ​(Round to four decimal places as​ needed.)
d. State the conclusion. (choose one from each ( x, y) set)
(Do not reject, Reject) Upper H0​, because the​ P-value is (greater than, less than, or equal to) the level of significance. There is
(sufficient, insufficient) evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to
10 beats per minute.

Answers

Answer:

H0 : σ²=10²

H1 : σ²>10²

χ² = 45.796

Pvalue = 0.2442

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Step-by-step explanation:

Given that :

Sample size, n = 41

Sample standard deviation, s = 10.7

Population standard deviation, σ = 10

Significance level, α = 0.10

The Hypothesis :

H0 : σ²=10²

H1 : σ²>10²

Using the χ² test for population variance :

The test statistic, χ² = (n-1)*s²/σ²

χ² = (41 - 1) * 10.7²/ 10²

χ² = (40 * 114.49) / 100

χ² = 4579.6 / 100

χ² = 45.796

The Pvalue ;

df = n - 1 ; 41 - 1 = 40

Pvalue(45.796, 40) = 0.2442

Since Pvalue > α ; WE fail to reject H0

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Paul can install a 300-square-foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take Paul and Matt to install the floor working together?
4 hours
9.9 hours
13.2 hours
30 hours

Answers

Answer:

9.9 hours

Step-by-step explanation:

The formula to determine the time together is

1/a+1/b = 1/c  where a and b are the times alone and c is the time together

1/18 + 1/22 = 1/c

The least common multiply of the denominators is 198c

198c(1/18 + 1/22 = 1/c)

11c+ 9c = 198

20c = 198

Divide by 20

20c/20 =198/20

c =9.9

Answer:

B - 9.9 hrs

Step-by-step explanation:

took the test.

What type of function is represented by the following table?

Number of weeks

1 2 3 4 5
Cost of rental car 79,
158,
237,
316,
395

Answers

Answer:

Linear

Step-by-step explanation:

cost = 79 * weeks

79*1=79

79*2=158

etc.

a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to fin​

Answers

Answer: It travels 560 miles per hour.

Step-by-step explanation:

using the proportion,

2660:4.75:x:1

or, 2660:4.75= x:1

or, 2660/4.75 = x/1

or, 2660 = 4.75x

or, x = 2660/4.75

so, x = 560

Answer:

Step-by-step explanation:

Bonjour,

4,75 h = 4+0,75*60 =

4h 45mn = 4*60 + 45 =240+45 => 265mn

265mn -> 2660 miles

1 mn -> 2660/265

60 mn -> (2660*60)/265=> 602,26miles/h

State and prove the Cantor Intersection Theorem.

Answers

Answer:

Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets.

Find the numerical value of the area under the normal curve given the following information:

to the right of z = 2.28

enter your answer as a decimal (NOT percentage) and lead with a zero...for example: 0.1234

Answers

Answer:

1 - 0.9887 = 0.0113

Step-by-step explanation:

There are 36 tables and 7 booths in the family restaurant. Each table seats 4 people. If the restaurant can seat up to 179 people, what is the capacity of each booth?

4 people

5 people

6 people

7 people

Answers

Answer:

5 people.

Step-by-step explanation:

First we need to find how many people 36 tables seats. In order to do this, we need to multiply 36 (tables) by 4 (people sitting) to get 144. Now just subtract 144 from 179 to see how many people are left, here we get 35. Since there are 7 booths, we divide 35 by 7 to get 5. Each booth holds 5 people.

(179-36x4)/7=5

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