Докажите тождество: sin⁴α - cos⁴α + cos²α - sin²α = 0

[latex]sin ^{4} a - cos^{4} a + cos^{2} a - sin^{2} a = 0 \\ (sin^{2} a-cos^{2} a )(cos^{2} a + sin^{2} a) +cos2a = \\ -1*(cos^{2} a -sin^{2} a)+cos2a=-cos2a+cos2a=0[/latex]