Question

What is the most reasonable first step in the proof of the identity below? (Multiple Choice)

Answer 1

cos(2 theta)=cos^4theta-sin^4theta

Answer 2

A. Write everything in terms of cos theta.
B. Set the left side of the identity equal to 0.
C. Divide each term by cos (2theta).
D. Factor cos^4theta-sin^4 theta as (cos^2theta+sin^2theta)(cos^2theta-sin^2theta)

Answer 3

Use the double angle formula to evaluate the left side first.

Answer 4

August your opinion about this ?

Answer 5

I was thinking the answer would be D. That I would factor and then later on divide by cos(2theta)

Answer 6

Once you rewrite the right side in terms of cos(theta) you may recognize a perfect square.

Answer 7

What's your reasoning?

Answer 8

so i think so exactly for the first step the D. choice too

Answer 9

I think a better answer would be A. Because if you rewrite everything in terms of cos(theta) it makes it simple and that implies that you already deduced that factorization and you got further.

Answer 10

Evaluating the right side of the equation by the factorization is a step comparable to simply evaluating the left side of the equation by the double angle formula. That is something you can do, but it might it's purpose is ultimately answer A.