How do you verify the identity of the following

Question

cos^2x-sin^2x = 1-2sin^2x

I am unsure how to do my homework, not looking for answers. Just want to know how to finish these identities. 

Answer 1

One thing you could do is make use of this identity, which you probably already know:

 

cos^2(x) + sin^2(x) = 1

 

If you solve this identity for cos^2(x), then substitute the result in the left-hand side of the equation you gave, then you get the right-hand side. Make sense?