Sin^2a-sin^2a×cos^2a=sin^4a доказать тождество

[latex] sin^{2} \alpha (1- cos ^{2} \alpha) = sin^{4} \alpha [/latex] [latex] sin^{2} \alpha - sin^{2} \alpha cos ^{2} \alpha = sin^{4} \alpha [/latex] [latex] sin^{2} \alpha ( sin^{2} \alpha+cos ^{2} \alpha - cos ^{2} \alpha) = sin^{4} \alpha [/latex] [latex] sin^{2} \alpha * sin^{2} \alpha= sin^{4} \alpha [/latex] [latex] sin^{4} \alpha = sin^{4} \alpha [/latex] Ч.Т.Д