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