Prove the identify on the left is equal to the right (sin x - cos x) (sin x + cos x^) = - cos x Solution (sinx-cosx)(sinx+cosx) = -cosx the identity you have proved is wrong you can verify it by substituting x = pi/4 sin(pi/4) = 1/sqrt(2) cos(pi/4) = 1/sqrt(2) sinx - cosx = 0 which makes lhs = 0 rhs = -cosx = -1/sqrt(2) so the identity is wrong..