Verify that each equation is an identity (1 - sin^(2)((x)/(2)))/(1+sin^(2)((x)/(2)))= (1+cosx)/(3-cosX)

Answers

Answer 1

Answer:

Given that we have;

[tex]sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }[/tex]

By the application of the law of indices and algebraic process of adding a and subtracting a fraction from a whole number, we have;

[tex]\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}[/tex]

Step-by-step explanation:

An identity is a valid or true equation for all variable values

The given equation is presented as follows;

[tex]\dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}[/tex]

From trigonometric identities, we have;

[tex]sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }[/tex]

[tex]\therefore sin^2 \left (\dfrac{x}{2} \right ) = \dfrac{1 - cos (x)}{2}[/tex]

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

[tex]1 + sin^2 \left (\dfrac{x}{2} \right ) = 1 + \dfrac{1 - cos (x)}{2} = \dfrac{2 + 1 - cos (x))}{2} = \dfrac{3 - cos (x))}{2}[/tex]

[tex]\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}[/tex]

[tex]\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}[/tex]


Related Questions

Our club has 10 members, and we need to appoint a president, a vice president, and a secretary. How many ways can we do this if: Each member can hold at most one office. Members can hole any number of offices

Answers

Answer: 720

Step-by-step explanation:

Given

A club has 10 members and needs one president, a vice president, and a secretary

There are 10 positions for president i.e. 10 ways to select a member for it

Similarly, there 9 persons left to choose a position for vice president

likewise 8 persons for secretary

Total no of ways to do it are

[tex]\Rightarrow 10\times 9\times 8\\\Rightarrow 720\ \text{ways}[/tex]

When writing a percent as a fraction, what
number do you write as the whole, or
denominator?

Answers

Answer:

100 is going to be the denominator or whole.

Step-by-step explanation:

A percent is basically equally to a number x/100

A truck bed has a volume of 120 cubic feet. The bed is 4 feet wide and has a height of
3 feet. What is the length of the bed?

Answers

Answer:

1440

Step-by-step explanation:

you have to do length x width x height

The telephone company offers two types of service. With Plan A, you can make an unlimited number of local calls per month for $18.50. With Plan B, you pay $6.50 monthly, plus 10 cents for each min. Of calls after the first 40 min. At least how many min would you have to use the telephone each month to make Plan A the better option?

Answers

Answer:

This is telling me that plan B is the better choice

for a certain number of minutes, but after that,

plan A is better.

Let +n+ = number of minutes of calls

with plan B

-----------------------------------------

Set up an equation that makes the 2 plans equal

and then add 1 more minutes to +n+

-----------------------------------------

plan A = plan B

+18.5+=+6.5+%2B+.1%2A%28+n+-+40+%29+

Step-by-step explanation:

Answer:

Plan A is better if you talk at least 121 minutes per month

Step-by-step explanation:

1. Plan B is $6.50 plus 10 cents for each minute

2. Plan A is $18.50

3. For plan A to be better, one need to spend over $12 extra

4. Each minute cost 10 cents, so $12 would be 120 minutes of talk

5. Plan A is better if you talk at least 121 minutes

Can someone please help me solve this. Also pls don’t give me a link.

Answers

The answer would be H.
To find this, use the quadratic formula.
x = 4 ± sqrt(-4)^2 - 4(2)(-5)/4
x = 4 ± sqrt 16+40/4
x = 4 ± sqrt 56/4
And that is your final answer!
H is the best answer and if you want it solved down I can give it to you too !

KaVaugn wants to solve the following system using the elimination method:

y = x − 6
y = -4x − 19

What number should the equation y = x − 6 be multiplied by to eliminate x? (4 points)

a
1

b
2

c
4

d
−6

Answers

I believe that the answer is C

Answer:

d.-6

Step-by-step explanation:

sana makatulong

help please
For each question order the cards from least to greatest. If the feature is equal to two or more functions, place them next to each other.Functions evaluated at x = -1
(put the cards/letters in order from least to greatest based on Functions evaluated at x = -1)

Answers

Answer:

Functions evaluated at x = -1

A. a(-1) = -2(-1) + 3 = 5

B. b(-1) = 0  (as per graph)

C. Find the equation first:

m = 4/8 = 1/2c(x) = 1/2x - 4c(-1) = -1/2 - 4 = -4.5

D.  d(-1) = (-1)² - 4 = -3

E. e(-1) = 2 (as per table)

F. f(-1) = 5/2 = 2.5 (as per graph)

G. g(-1) = 2(3)⁻¹ - 2 = 2/3 - 2 = - 1 1/3

H. h(-1) = 2 (as per table)

The order:

C >> D >> G >> B >> E and H >> F >> A

PLEASE HELP!!!!!!! NEED THIS ASAP

Answers

Answer:

174

Step-by-step explanation:

72+72+10+20+ 174

Does anyone know how to find the volume of a cylinder?​

Answers

Answer:

V=πr2h

you could've searched this up but i hope this helps anyway

Write An Equation in Point-slope form for the line through the given point with the given slope "(-7,9);m=4/5"​

Answers

Answer:

y-9=4/5(x+7)

Step-by-step explanation:

Point slope for is y-y1=m(x-x1). In this case, y1 is 9, x1 is -7, and m is 4/5. Therefore, we can fill in this equation. The equation will be y-9=4/5(x--7) This is equal to y-9=4/5(x+7).

If this helps please mark as brainliest

What is the percent of each? Please help!!

Answers

Answer:

1 Cards = 36%

2 Cards = 28%  

3 Cards = 24%

4 Cards = 12.5%

Step-by-step explanation:

-------------------------

Answers

Answer:

1 < x < 12

Step-by-step explanation:

The triangles satisfy the Converse Hi nge Theorem Condition the two triangles have two corresponding equal sides. Thus, the included angle of the triangle that has the largest length of the third side is greater than the included angle of the other triangle with a lesser third side length.

Thus,

33 > 3x - 3

Solve for x

33 + 3 > 3x - 3 + 3

36 > 3x

36/3 > 3x/3

12 > x

To ensure the angle is not 0 or negative, thus:

3x - 3 > 0

Solve for x

3x - 3 + 3 > 0 + 3

3x > 3

3x/3 > 3/3

x > 1

Possible range of values of x would be:

1 < x < 12

please please help! :)

Answers

Answer:

assuming the shape is a square

1. 90 degrees

2. 45 degrees

3. 45 degrees

4. 90 degrees

Step-by-step explanation:

maths and angles

Help with this Math problem!

Answers

Answer:

what is the question which you are asking can you please tell

1). 2-(-5)-3
2). (-7)-(-7)-4
3). (-5)-6-(-6)
4). 6-(-3)-1

Answers

1. 4

2. -4

3. -5

4. 8

 

URGENT MARKING BRAINLIEST

Answers

Answer:

for the first questions: 36%

Step-by-step explanation:

To answer the first question: What percent of people chose Mexican food?

Number of people who choose mexican food: 27

Total number of people who took the survey: 24 + 27 + 9 + 15 = 75

So, 27 out of 75 people choose mexican food, or in other words 27/75. If you divide 27/75, you get the decimal 0.36. This decimal is the same thing as 36%.

The steps for the other three questions are the same.

(2^3//4^2)^5 What is the equivelant expression?

Answers

Answer:

A

Step-by-step explanation:

This is the same as ((2^3)/(4^2))*((2^3)/(4^2))*((2^3)/(4^2))*((2^3)/(4^2))*((2^3)/(4^2)) which is equal to (2^(3+3+3+3+3)/4^(2+2+2+2+2)), so its (2^15/4^10)

Answer:

You could say 10/15-12/15.

Step-by-step explanation:

Solve for x. Round your answer to the nearest tenth

Answers

Answer:

6.1

Step-by-step explanation:

tan 27° = x/12

x = 12 · tan 27°

x = 6.1



What is the value of the expression 4(80+ b) - 12, where b=20?
Α. 328

Β. 352
C. 388

D. 412

Answers

Answer:

B. C which is the answer.

Answer:

Step-by-step explanation:

c=388

60/3[150+2{6+3(17-14)}}
11. 56-45-5(90-3[4-(25-31)}]

Answers

Answer:

.4635.30967741

Step-by-step explanation:

hope this helps

Sam has 1 3/4 quarts of orange juice.
He is pouring it into glasses that
each hold 1/4 quart. How many glasses can he fill?
glasses can he fill?

Answers

He can fill 7 glasses because 1/4 can go into 3/4, three times and 1/4 can go into 1, four times ( 1 is the same as 4/4) then add 3+4 which equals 7.

3 × 70° 45' 30" - 2 × 40° 25' 10"

Answers

Answer:

Step-by-step explanation:

3×70° 45' 10''-2×40°25'10''

=210° 135'30''-80° 50'20''

=130°85'10''

=131°25'10''

Solve for xx. Leave your answer in simplest radical form.
3
8
x
2


ANSWER ) x = sqrt51

Answers

This answer is 76 let me know if I’m wrong

For school lunch students have 3 meat choices (beef, chicken, or fish), 2 potato choices (mashed or fried), and 3 drink choices (milk, juice, or water).

How many different combinations could students create using one meat, one potato, and one drink?
- 8
- 9
- 11
- 15
- 18

Answers

Answer:

18

Step-by-step explanation:

[tex]3 \times 2 \times 3[/tex]

That will give you 18 which is the answer

18 , if you multiply 3 x 3 x 2 = 18

What is the answer? I am really confused so if you can please explain it.

Answers

Answer:

Step-by-step explanation:

Answer:   9/25  of a mile

=========================================================

Explanation:

Multiply the fractions 9/10 and 2/5 to get

(9/10)*(2/5)

(9*2)/(10*5)

18/50

9/25

---------------------

Here's a visual way to see what's going on. Start by drawing a rectangle of any size or shape. Cut the rectangle vertically into 10 equal slices. Then shade 9 of those slices to represent the fraction 9/10, which is how far (in miles) Lewis walked. See the diagram below. Specifically, refer to figure 1.

The friend walked 2/5 of this shaded amount. Draw 4 horizontal lines to split each vertical bar into 5 equal pieces. So we'll be forming a grid of smaller rectangles. For any given column, you'll shade exactly 2 smaller rectangles out of the 5 total. Hence the 2/5. This is shown in yellow in figure 2. The yellow region is 2 units tall by 9 units across, so we have 2*9 = 18 yellow rectangles in all. This is out of 5*10 = 50 smaller rectangles overall.

That's how we get to the fraction 18/50 which reduces to 9/25 when you divide both parts by the GCF 2.

PLEASE HELP! I am just learning functions. Any tips?

Answers

Answer:

Step-by-step explanation:

value is decreasing so rate should be <1

f(x)=Pr^x

=1250 (0.8)^x

if x=1

f(1)=1250(0.8)^1=1000 $

if x=2

f(2)=1250(0.8)^2=800 $

if x=3

f(3)=1250(0.8)^3=640  $

so D is the correct answer.

HELP IM BEING TIMEDDD THANK YOU

Answers

Answer: A and C!

yw :DD\

i need help with this question

Answers

The question isn’t up there.

Math question due today. 20 points.


A bathtub is the shape of a rectangular prism. The dimensions are 5 1/4 ft x 2 1/2 ft x 2 3/4 ft. What is the volume of the bathtub?


A. 10 1/2 ft
B. 36 3/32 ft
C. 14 7/16 ft
D. 13 1/8 ft

(No photo provided.)

Answers

Answer: 36 3/32 so the answer is B.

Step-by-step explanation:

Your answer is B.) 36 3/32
Explaantion:
The formula for volume of a rectangular prism is length x width x height.

Have a nice day.

Help me, please!!!!!!!!!

Answers

Answer:

x ≈ 17.32, y = 20

Step-by-step explanation:

sin (30°) = 10/y

=> y = 10/sin (30°)

=> y = 20

x = [tex]\sqrt{20^{2} - 10^{2}}[/tex]

=> x ≈ 17.32

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