Use a double-angle or half-angle formula to simplify the given expressions: 1. If cos^2(39degrees)-sin^2(39degrees) = cosA then what does A equal? 2. If cos^2(3x)-sin^2(3x) = cosB, what does B equal?

Question

I'm just beginning to learn about the double and half angle formulas. However, with these I don't know where to begin. For A it looks like I'm supposed to be using...

Sin^2x=(1-cos^2x)/2 and cos^2x=(1+cos2x)/2 and then subtract those two results from one another? I'm confused on how to get rid of 39 degrees. What angles would I be adding or subtracting to get to it?

As for the second problem, I'm lost with how to handle the 3.

Detailed explanations are very appreciated! I want to understand the material so I can do similar problems myself. Thanks so much in advance!

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Answer 1 · 2017-10-15T05:46:11

# 1. cos 78^@, and, 2. cos 6x.#

We have, #cos^2theta-sin^2theta=cos2theta.#

#:. cos^2 39^@-sin^2 39^@=cos(2(39^@))=cos78^@..........(1).#

Similarly, #cos^2(3x)-sin^2(3x)=cos(2(3x))=cos6x..........(2).#