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Question

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

4)105 °.

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

Answer 1

(4)

Step 1:

The trigonometric value is .

Rewrite value as .

Since  .

Substitute the values of  and .

Solution :

.

Answer 2

(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  .