Which function represents the graph? Y=-cos(x) y=-sin(x)y=cos(x)y=sin(x)

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

Allisa [31]

Answer:

Given that we have;

$sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }$

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

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

Step-by-step explanation:

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

The given equation is presented as follows;

$\dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

From trigonometric identities, we have;

$sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }$

$\therefore sin^2 \left (\dfrac{x}{2} \right ) = \dfrac{1 - cos (x)}{2}$

$1 - sin^2 \left (\dfrac{x}{2} \right ) = 1 - \dfrac{1 - cos (x)}{2} = \dfrac{2 - (1 - cos (x))}{2} = \dfrac{1 + cos (x))}{2}$

$1 + sin^2 \left (\dfrac{x}{2} \right ) = 1 + \dfrac{1 - cos (x)}{2} = \dfrac{2 + 1 - cos (x))}{2} = \dfrac{3 - cos (x))}{2}$

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

3 0

3 years ago

Work out the surface area of this solid prism.

zhannawk [14.2K]

THE SURFACE AREA IS 3220CM^2

3 0

2 years ago

the first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. together they charged a total of $1300. wha

abruzzese [7]

Answer:

1st mechanic charges $55 per hour

2nd mechanic charges $50 per hour

Step-by-step explanation:

Suppose rate charged per hour for first meachnic is "x"

rate charged per hour for 2nd mechanic is "y"

So,

1st mechanic 10 hrs, 2nd mechanic 15 hrs, total charge 1300, so we can write:

10x + 15y = 1300

Also, total hourly rate of both is 105, so we can write:

x + y = 105

or

x = 105 - y

We can substitute this into 1st equation and solve for y:

$10x + 15y = 1300\\10(105-y) + 15y = 1300\\1050-10y+15y=1300\\5y=250\\y=50$

And x is:

x = 105 - y

x = 105 - 50

x = 55

1st mechanic charges $55 per hour

2nd mechanic charges $50 per hour

5 0

3 years ago

Five multiples of 3 that are not in the product game board

Kruka [31]

The answer is 1,3 you can check

4 0

4 years ago

PLEASE HELP TOP ANSWER GETS BRAINLIEST!! ***Solve for m: 3.2(4m + 10) – (-7.2m) = 37 ***!!!!!!!

alisha [4.7K]

Answer:

1/4 or 0.25

Step-by-step explanation:

3.2(4m + 10) – (-7.2m) = 37
12.8m+32+7.2m=37
20m= 37-32
20m=5
m=5/20= 1/4 or 0.25

7 0

4 years ago