Cos^4a+2sin^2a-sin^4a=1

[latex] cos^{4} \alpha +2 sin^{2} \alpha -cos ^{4} \alpha =1 ( cos^{4} \alpha - sin^{4} \alpha )+2sin^{2} \alpha =1 ( cos^{2} \alpha + sin^{2} \alpha )*( cos^{2} \alpha - sin^{2} \alpha )+2 sin^{2} \alpha =1 [/latex] [latex]1*( cos^{2} \alpha - sin^{2} \alpha )+2 sin^{2} \alpha =1 sin ^{2} \alpha + cos^{2} \alpha =1 1=1 [/latex] ч.т.д.