Use the fundamental identities and algebraic techniques to p

Use the fundamental identities and algebraic techniques to prove the following identities.

Use the fundamental identities and algebraic techniques to prove the following identities. (sin x + cos x)^4 = (1 + 2 sin x cos x)^2

Solution

(sin x + cos x)^4 = (1 + 2*sin x*cos x)^2

LHS = (sin x + cos x)^4 = [(sin x + cos x)^2]^2

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

        = (1 + 2*sin x*cos x)^2 = RHS