Question

I need to use a double angle or half angle formula to simplify the given expression in the photo

Answer 1

According to the double-angle identity:

`\cos (2C)=\cos ^2C-\sin ^2C`

So, let's solve (a):

(a) Given:

`\cos ^2(30)-\sin ^2(30)=\cos (A)`

Comparing with the identity:

C = 30°

Then, 2C = 2*30 = 60°

Since

A = 2C, A = 60°

Answer: A = 60°.

(b) Given,

`\cos ^2(2x)-\sin ^2(2x)=\cos (B)`

Comparing with the identity:

C = 2x

2C = 2*2x = 4x

Then,

B = 2C = 4x

Answer: B = 4x°.

In summary,

(a) A = 60°.

(b) B = 4x°.