Докажите тождество: [latex] \frac{cos ^{2} \alpha - sin^{2} \alpha }{ctg \alpha -tg \alpha } =sin \alpha *cos \alpha [/latex]

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