(tg²a-sin²a)*ctg²a=sin²a доказать

[latex](tg^2 \alpha -sin^2 \alpha)*ctg^2 \alpha =sin^2 \alpha ;[/latex] [latex]tg^2 \alpha*ctg^2 \alpha -sin^2 \alpha*ctg^2 \alpha =sin^2 \alpha ;[/latex] [latex]1 -sin^2 \alpha* \frac{cos^2 \alpha }{sin^2 \alpha} =sin^2 \alpha ;[/latex] [latex]1 -cos^2 \alpha =sin^2 \alpha ;[/latex] [latex]sin^2 \alpha =sin^2 \alpha ;[/latex]