ДОКАЖИТЕ ТОЖДЕСТВО: [latex] \frac{1+cos2a}{1-cos2a} =ctg ^{2} a[/latex]

[latex]\frac{1+\cos2 \alpha }{1-\cos2 \alpha }=\frac{\cos^2 \alpha +\sin^2 \alpha +(\cos^2 \alpha -\sin^2 \alpha )}{\cos^2 \alpha +\sin^2 \alpha -(\cos^2 \alpha -\sin^2 \alpha )}=\frac{\cos^2 \alpha +\sin^2 \alpha +\cos^2 \alpha -\sin^2 \alpha }{\cos^2 \alpha +\sin^2 \alpha -\cos^2 \alpha +\sin^2 \alpha }=\\\\=\frac{2\cos^2 \alpha }{2\sin^2 \alpha }=(\frac{\cos \alpha }{\sin \alpha })^2=ctg^2 \alpha .[/latex]