Question

Prove the identity cos^4 A - cos^2 A = sin^4 A - sin^2 A

Answer 1

$\cos ^{4} (x) - \cos ^{2} (x) \\ = (\cos ^{2} (x) )^{2} - \cos ^{2}(x) \\ = (1 - \sin^{2} (x)) ^{2} - (1 - \sin ^{2} (x) ) \\ = 1 - 2 \sin ^{2} (x) + \sin ^{4} (x) - 1 + \sin ^{2} (x) \\ = \boxed{\sin ^{4} (x) - \sin ^{2} (x)}$

Answer 2

Here is your answer with explanation