1-sinA+cosA / sinA+cosA-1 = 1+cosA/sinA​

Answers

Answer 1

Solution:

[tex]\dfrac{\left[\left(\sin ^{2} A+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]\right.}{\left[\left(1-\cos ^{2} A\right)-(1-\cos A)^{2}\right]}[/tex]

[tex]\dfrac{\left[\left(1-\cos ^{2} A\right)+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]}{\left[(1-\cos A)(1+\cos A)-(1-\cos A)^{2}\right]} [/tex]

[tex]\dfrac{(1-\cos A)[1+\cos A+2 \sin A+1-\cos A]}{[1-\cos A][1+\cos A-1+\cos A]} [/tex]

[tex]\dfrac{[2+2 \sin A]}{[2 \times \cos A]}[/tex]

[tex]\dfrac{2(1+\sin A)}{2 \times \cos A}[/tex]

[tex]\dfrac{1+\cos A}{\sin A} [/tex]

Hence Proved.


Related Questions

Choose the correct simplification of the expression (2x7y)2(y5)3.

Answers

The correct simplification of the expression is  4x¹⁴y¹⁷

Given,

The expression is (2x⁷ y)² (y⁵)³

To distribute the exponent, apply the power rule (ab)ⁿ = aⁿbⁿ

Implement the product rule to (2x⁷y)².

Here, we have a = 2x⁷ , b = y and n = 2

=(2x⁷)² y²(y⁵)³

= 2²(x⁷)² y²(y⁵)³

= 4(x⁷)² y²(y⁵)³

Now exponents should be multiplied while using the product rule.

The product rule is (aˣ)ⁿ = aˣⁿ

We apply this to (x⁷)² and (y⁵)³

So the expression becomes,

=4x⁷·² y² (y⁵·³)

= 4x¹⁴ y² y¹⁵

∵ In exponents we have a rule that if bases are same then powers are added i.e, aˣ aⁿ = aˣ⁺ⁿ

∴ 4x¹⁴ y¹⁵ ⁺ ²

= 4x¹⁴ y¹⁷

Hence we get the answer as 4x¹⁴ y¹⁷

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How many complex roots does the equation 0=3x5−x4−5x2+1 have?

Answers

the equation has 5 complete roots

5

The given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.

What is a polynomial?

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The given polynomial equation below is:

0 = 3x⁵ − x⁴ − 5x² + 1

3x⁵ − x⁴ − 5x² + 1 = 0

The given polynomial equation is a polynomial of degree 5.

The simplest method is to solve it graphically using a graphing program.

Clearly, the polynomial equation is a degree 5 equation, hence it has a maximum of 5 roots.

We may now locate the roots of the equation using the graph.

Since there are 3 real roots, the remaining are two complexes, so there are 2 complex roots

Hence, the given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.

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What is the solution to the following equation?
3(x-4)-5-x-3
A. x = 12
B. x=3
C. x=8
D. x = 7

Answers

Answer:

D. x = 7

Step-by-step explanation:

NOTE : there should be an equal sign somewhere in the given expression.

suppose the equation is the following:

3(x-4)-5 = x-3

………………………………………………………

3(x - 4) - 5 = x - 3

⇔ 3x - 12 - 5 = x - 3

⇔ 3x - 17 = x - 3

⇔ 3x - 17 + 17= x - 3 + 17

⇔ 3x = x + 14

⇔ 2x = 14

⇔ x = 14/2

⇔ x = 7



15. 3x-5=3
16. 3(x-2) = 4(x + 3)
17. +3=
18. 2==
19. 4-2-3
X+2
20.-2-3-3
21. 쭉 = 큭
22. 2x-5-1=3-x
3. 2x + ==3(x-1)
4. 10x-1=x+4
5. k=8k-2
6. -x + 2 = 3x-27
4
7. 1-6x = -x +
B.
9. 2-(x + 1) = 2 + 5x
D. 2(1-x) = 10 - (x + 2)
. 9x - (4x - 5) = 3x - 11
x-9=3(x + 1)
-xx-2)-4=x+6▸
+ 2x
6(5-4x) = -4(5x + 11)

Answers

Answer:

tgnjfgznjE XVNJ

Step-by-step explanation:

rtjtejWEJAREfnndzjt

Answer:

15. 2.66

16. - 18

17. Impossible

18. Impossible

19. - 1

20. - 8

21.

Question 1 of 10
Solve 10x+16 ≥ 6x+ 20.
O A. x29
OB. x≤ 1
OC. x2 1
OD. x≤ 9

Answers

Answer: I think B. Explain:

please help i dont know how to do this

Answers

First you have to do the ones in the brackets

Graph the function.
For the function whose graph is shown below, which is the correct formula for the function?

Answers

Answer:

[tex]\displaystyle{y=-3x-1}[/tex]

Step-by-step explanation:

I have two methods: standard-learning which will explain overall mathematically - basically formula, etc. - while the other one trick-tips method will rely on choices rather mathematical calculations but with explanation on why and how.

Standard-Learning

First, let’s pick two points that are integers since they are easily to be found via graphs. We see that (-1,2) and (0,-1) is a part of the graph so now we finally have picked two points for our calculations.

When we have finally picked two points, we will be using them for slope calculation. This part is crucial for finding an equation of a line because a line has to contain slope in its equation.

To calculate the slope, we use rise over run formula which is:

[tex]\displaystyle{\dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Note that [tex]\displaystyle{\Delta}[/tex] is delta - in both mathematic and physics, it means changes in.

So, we will be using those two points that we have picked to substitute in the slope formula. Let’s determine that [tex]\displaystyle{(x_2,y_2)=(-1,2)}[/tex] and [tex]\displaystyle{(x_1,y_1)=(0,-1)}[/tex].

Therefore, our slope will be:

[tex]\displaystyle{m=\dfrac{2-(-1)}{-1-0}}\\\\\displaystyle{m=\dfrac{2+1}{-1}}\\\\\displaystyle{m=-3}[/tex]

Next, find the y-intercept. From the graph, we see that the graph intercepts at (0,-1) which is y-intercept so we will only use y-value. Hence, b = -1.

From the slope-intercept form:

[tex]\displaystyle{y=mx+b}[/tex]

Substitute m (slope) = -3 and b (y-intercept) = -1. Hence, the equation of line is:

[tex]\displaystyle{y=-3x-1}[/tex]

Fast Way (Trick-Tips)

Relying on choices and knowledge of graph, notice that there are slopes of 3 and -3.

Keep in mind that if slope is negative, it will decrease down and if slope is positive, it will increase up.

Therefore, cut off all choices with positive slopes which are 1 and 3. We are now left with 2 and 4.

Next, look at the graph and tell its y-intercept. It intercepts y at y = -1 so we take value of -1.

So choice 4 is cut off and now we have choice 2 as the answer.

Learn More:

https://brainly.com/question/27514958 - Find the line equation with given points

(x - 4)/(x + 6) - (x - 6)/(x + 4)​

Answers

Answer:

[tex]\frac{20}{(x+4)(x+6)}[/tex]

Step-by-step explanation:

assuming you require the expression simplified

[tex]\frac{x-4}{x+6}[/tex] - [tex]\frac{x-6}{x+4}[/tex]

multiply the numerator/denominator of the first fraction by (x + 4)

multiply the numerator/denominator of the second fraction by (x + 6)

= [tex]\frac{(x-4)(x+4)}{(x+4)(x+6)}[/tex] - [tex]\frac{(x-6)(x+6)}{(x+4)(x+6)}[/tex] ← expand and simplify numerators leaving the common denominator

= [tex]\frac{x^2-16-(x^2-36)}{(x+4)(x+6)}[/tex]

= [tex]\frac{x^2-16-x^2+36}{(x+4)(x+6)}[/tex]

= [tex]\frac{20}{(x+4)(x+6)}[/tex]

In AABC, what is the value of x?

Answers

Answer:

x = 6.5

Step-by-step explanation:

* since it's a triangle ALL the angles inside should give you 180° * Equate everything to 180°

8x + 10x - 10°+ 10x + 8° = 180°( sum of angles on a triangle)

28x - 2° = 180° * group like terms*

28x = 182°

x = 6.5

Raya buys a van for £9500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £665 each month.
Find the ratio of the deposit Ray pays to the total of the 12 equal payments.
Give your answer in its simplest form.

Answers

Step-by-step explanation:

yo thara bhai joginder tu he ek bndr

find the new prices after the given percentage increases.
a] £35 increased by 10%
b} £105.99 increased by 12%

Answers

Answer:

a] 38.5$
b] 118.71$

Step-by-step explanation:

A)35$ was increased by 10%
So:
10% of 35$
10/100 x 35 ($)
3.5$
So 35$ was increased by 3.5$ and the new price is 38.5$
B)105.99$ was increased by 12%
So:
12% of 105.99$
12/100 x 105.99$
=12.7188$
Let's round it to the nearest hundredths:
12.72$

So 105.99$ was increased by 12.72$ and the new price is 118.71$

HOPE IT HELPS :D
Tip: "of" means multiplication in Maths.

What is 9 squared?
Why?
Why do we call this "Squared"?
What is 5 cubed?
Why?
Why do we call this "Cubed"?

Answers

Answer:

The squared root of 9 is 3

Why - Half of 9 is 3

Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.

5 Cubed is equal to 125

Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5

Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.

The first step in determining the solution to the system of equations, y = -x2 - 4x - 3 and y = 2x + 5, algebraically is to set the two equations equal as -x2 - 4x -3 = 2x + 5. What is the next step?

Answers

Answer:

See below

Step-by-step explanation:

Next step is to gather 'like' terms

-x2 - 4x -3 = 2x + 5.

x^2 + (4x + 2x)   + (3+5)    = 0       then simplify

x^2 + 6x + 8     = 0        then factor

(x+4)(x+2) = 0  

so either of these terms = 0

x+4 = 0    means   x = -4

x+ 2 = 0 means  x = - 2          

Answer:

d

Step-by-step explanation:

Combine like terms onto one side of the equation.

If p() = x2 - 1 and q(x) - 5(x-1), which expression is equivalent to (p - q)(x)?

Answers

Answer:

[tex]\text{If p(x) = x2 - 1 and q(x) = 5(x - 1), the expression which is equivalent to}[/tex] [tex]\text{ (p - q)(x) is (x2 - 1) - 5(x - 1).}[/tex]

Step-by-step explanation:

Given:

p(x) = 2x2 - 1q(x) = 3(x - 1)

To find:

(p - q)(x)

We know:

(p - q)(x) = p(x) - q(x)

Substitute

(2x^2 - 1) - 3(x - 1)

[tex]\text{Therefore, the expression equivalent to (p - q)(x) is (2x2 - 1) - 3(x - 1).}[/tex]

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive. Mr. McMillan has already taught his class 8 letters. The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters. Mr. McMillan plans to teach his class 4 new letters per week, and Ms. Burke intends to cover 3 new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?

Answers

The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.

Mr. McMillan has already taught his class 8 letters.

The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.

Mr. McMillan plans to teach his class 4 new letters per week.

Ms. Burke intends to cover 3 new letters per week.

Eventually, the students in both classes will know how to write the same number of letters.

Then the number of weeks by which the students in both classes will know how to write the same number of letters will be

Let x be the number of the weeks and y be the total number of the letters.

Then the equation will be

y = 4x + 8 …1

y = 3x + 12 …2

Then by solving the equations 1 and 2, we have

x = 4 and y = 24

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2x + 5y = 17 6x - 5y = -9

Answers

Answer:

Step-by-step explanation:

which statement is true about fiction ​

Answers

Answer:

The function is even because of symmetry over x axis

Yaqub, Angus and Iris share 18 slices of pizza in the ratio
1:3:2.
How many slices of pizza does Iris have?

Answers

Answer:

6 Slices

Step-by-step explanation:

Total units = 1 + 3 + 2 = 6 Units

6 Units = 18 Slices of Pizza

Iris shared 2 units.

1 Unit = 18/6 = 3 Slices of Pizza

2 Units = 2 * 3 = 6 Slices of Pizza

Choose any set of Pythagorean triplets of your choice and illustrate them using graph sheet.
Example given below:

Answers

The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.

What are Pythagorean triplets?  

In a right angled triangle, its side, such as hypotenuse, perpendicular and base  is Pythagorean triplets.

We have

Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.

[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]

and c = 13

Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.  

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HELP !!!
Which of the following best describes the slope of the line below?
• A. Negative
O B. Zero
• C. Positive
D. Undefined

Answers

The answer to this is negative

Which ordered pair would form a proportional relationship with the point graphed below?


On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)

Answers

Answer:

(5,20)

Step-by-step explanation:

divide both sides of (10, 40) by the same number 2 and you will get (5,20). The points should all lie on the same straight line to form a proportional relationship.

Answer: 5,20

Step-by-step explanation:

If 1=3 2=3 3=5 4=4 5=4 then 6=?​

Answers

The value of the 6 is 3.

If you write 1 in word then you will write one and if you count the letter it will give you 3

Similarly, if you write the numbers 2,3,4,5 in word and count the number you will get 3,5,4,4 respectively.

What are the counting letters?

counting Letters provides a perfect way to introduce number words to beginning readers, as well as discuss the concepts of letters and words.

So, if you write 6 in words you will write six and on counting the letter you will get 3.

Hence, 6 = 3 ans.

Therefore the value of the 6 is 3.

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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.

2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4

Answers

Answer:

2.3p – 10.1 = 6.49p – 4  [tex]\huge \checkmark[/tex]

230p – 1010 = 650p – 400 – p  [tex]\huge \checkmark[/tex]

Step-by-step explanation:

……………………………………………

2.3p – 10.1 = 6.5p – 4 – 0.01p

⇔ 2.3p – 10.1 = (6.5p – 0.01p) – 4

⇔ 2.3p – 10.1 = (6.5 – 0.01)p – 4

⇔ 2.3p – 10.1 = (6.49)p – 4

⇔ 2.3p – 10.1 = 6.49p – 4

_______________________

_______________________

2.3p – 10.1 = 6.5p – 4 – 0.01p

⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)  multiply both sides by 100

⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)

⇔ 230p – 1010 = 650p – 400 – p

……………………………………………………

i need help i don’t know how to solve these!

Answers

Its actually pretty simple, all you do is graph both inequalities and wherever both of the shaded areas overlap is where all of the solutions will be. Hope this helps

Jose paid $1.12 for a dozen eggs at his local grocery store. Determine the cost of 18 eggs.

Answers

Answer:

$1.68

Step-by-step explanation:

1 dozen is 12.

18 is the same as 12 + 6

6 eggs is half of 12 eggs.

Since 12 eggs cost $1.12, then 6 eggs cost half of $1.12, or $1.12/2 = $0.56.

18 = 12 + 6, so

the price of 18 eggs = the price of 12 eggs + the price of 6 eggs.

price of 18 eggs = $1.12 + $0.56 = $1.68

Match the verbal expression (term) with its algebraic expression (definition).

Match Term Definition
d
Some number increased by two A) a ÷ 2
c
A variable decreased by two B) y2
e
Product of an unknown value and two C) x − 2
2
Quotient of some number and two D) b + 2
b
An unknown value squared E) 2z

Answers

The matching of definitions and terms are done below.

Some number increased by two ⇒ b + 2A variable decreased by two ⇒ x – 2Product of an unknown value and two ⇒ 2zQuotient of some number and two ⇒ a ÷ 2An unknown value squared ⇒ y²

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Match the verbal expression (term) with its algebraic expression (definition).

Some number increased by two ⇒ b + 2

A variable decreased by two ⇒ x – 2

Product of an unknown value and two ⇒ 2z

Quotient of some number and two ⇒ a ÷ 2

An unknown value squared ⇒ y²

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Match each inequality to the number line that represents its solution:

Answers

Step-by-step explanation:

I have solve all the questions and your work is to match with that option

Use the fraction model to multiply: three multiplied by five sevenths. Leave your answer as an improper fraction. (1 point)

three fraction models, each model is partitioned into seven equal parts, with five parts shaded in each model
eight sevenths
eight tenths
fifteen twenty ones
fifteen sevenths

Answers

The product of three and five-sevenths is given by (D) Fifteen sevenths.

In fraction multiplication, we multiply the corresponding position like we multiply numerator with numerator and denominator with another denominator.

The denominator for a whole number is always 1.

Here given the numbers are three and five-sevenths, that is [tex]3,\frac{5}{7}[/tex].

So here since 3 is a whole number then the denominator of it is 1.

We can write 3 as [tex]\frac{3}{1}[/tex].

So product [tex]=\frac{5}{7}\times\frac{3}{1}=\frac{5\times3}{7\times1}=\frac{15}{7}[/tex]

Using the fraction model we get,

Here we can see that there are three bars with seven divisions in which fives are shaded.

So in multiplication with three we have to take the shaded region as the numerator and have to all the shaded and total bar for once.

here a total number of divisions in one bar is 7, so the denominator of the product is 7.

A total number of shaded divisions is 15, so the numerator of the product is 15.

So the product is [tex]\frac{15}{7}[/tex], that is fifteen sevenths.

Hence the correct option is (D) Fifteen sevenths.

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The Law of Sines states that sin A/b = sin B/c = sin C/a

True
False

Answers

False
Law of signs is
SinA = SinB = SinC
——- ——- ———
a. b. c.
A= angle A
a= length of side A
B= angle B
b= length of side B
C= angle C
c= length of side C

Step-by-step explanation:

hope you can understand

Expand & simplify
3(t+5)+5(t−6)

Answers

Answer:

8t - 15

Explanation:

⇒ 3(t+5)+5(t−6)

distribute inside parenthesis

⇒ 3(t) + 3(5) + 5(t) + 5(-6)

multiply the variables

⇒ 3t + 15 + 5t - 30

collect like terms

⇒ 3t + 5t + 15 - 30

add/ subtract like terms

⇒ 8t - 15

Solution: 8t-15

Detailed explanation:

First the problem asks us to expand

[tex]\tt 3(t+5)=3\cdot t +3\cdot5=3t+15[/tex]

Similarly

[tex]\tt 5(t-6)=5\cdot t -5\cdot 6=5t-30[/tex]

Therefore

[tex]\tt 3t+15+5t-30[/tex]

Upon combining like terms

[tex]\tt 8t+15-30[/tex]

Upon doing this further

[tex]\tt 8t-15[/tex]

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