Question

simplify cos^2 5a- sin^2 5a

Answer 1

cos^2(5a) = 1-sin^2(5a), so 1-2sin^(5a)= cos^2(5a)-sin^2(5a). There are some other identities that can be used, but it really all depends what you are seeking the final result for that determines what you want to use. There are sum and product id's pythagorean Id's, double and half angle Id's , but this gets it to one tirg function in the eq.