help please.

Question

Use the angle sum identity to find the exact value of each.

1)cos 105° 

2)sin 195° 

Use the angle difference identity to find the exact value of each.

 

 3) cos 750

4) sin 1050

 5) Show sin 4θ = 4sin θ cos θ cos 2 θ

6) Solve 5 cos 2 θ = 1 for 0o < θ < 360o

7) Solve cos^2 θ = cos θ for 0o < θ < 360o

8) Solve cos 2 θ = cos θ + 2 for 0 < θ < 2p

 

Answer 1

Step 1:

The trigonometric value is .

Rewrite value as .

Since  .

Solution :

.

Answer 2

Step 1:

The trigonometric value is .

Rewrite value as .

Since  .

Step 2:

Rewrite .

.

Since  .

Rewrite .

.

Since  .

Step 3:

Solution:

.

Answer 3

(3)

Step 1:

The trigonometric value is .

Rewrite value as .

Since  .

Substitute the values of  and .

Solution :

.

Answer 4

Step 1:

The trigonometric value is .

Rewrite value as .

Since  .

Substitute the values of  and .

Solution :

.

 

Answer 5

(5)

Step 1:

The trigonometric expression is .

Rewrite  .

Since  .

Step 2:

Rewrite  .

Substitute above expression in .

Solution :

.

Answer 6

(6)

Step 1:

The trigonometric expression is .

Divide each side by .

The general solution of is ,where is integer.

Divide each side by .

if then .

if then .

if then .

The solution of the given expression are and in the interval .

Solution :

and .

Answer 7

(7)

Step 1:

The trigonometric expression is .

Rewrite .

The general solution of is ,where is integer.

Step 2:

Case 1:

if then .

if then .

is out of the interval.

Case 2:

if then .

if then .

are out of the interval.

The solution of the given expression are in the interval .

Solution :

.

Answer 8

(8)

Step 1:

The trigonometric expression is .

Use the trigonometric identity .

The range of  is .

So .

.

Step 2:

The general solution of is ,where is integer.

.

if then .

if then

is out of the interval .

The solution of the trigonometric expression is in the interval .

Solution :

The solution of the trigonometric expression is  .