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Решите задачу:

$1)1-cos^2 \alpha =sin^2 \alpha \\ \\ 2) \frac{1-cos^2 \alpha }{sin \alpha* cos \alpha }= \frac{sin^2 \alpha }{sin \alpha* cos \alpha} = \frac{sin \alpha }{cos \alpha } =tg \alpha \\ \\ 3)tg \alpha +ctg \alpha = \frac{sin \alpha }{cos \alpha } + \frac{cos \alpha }{sin \alpha } = \frac{sin^2 \alpha +cos^2 \alpha }{sin \alpha* cos \alpha } = \frac{1}{sin \alpha* cos \alpha}$

$4)sin^2 \alpha * \frac{1}{sin \alpha *cos \alpha } = \frac{sin \alpha }{cos \alpha } =tg \alpha$

$\frac{1-cos^2 \alpha }{sin \alpha* cos \alpha } -sin^2 \alpha (tg \alpha +ctg \alpha )=0 \\ \\ \frac{sin^2 \alpha }{sin \alpha* cos \alpha} -sin^2 \alpha * \frac{1}{sin \alpha* cos \alpha} =0 \\ \\ \frac{sin \alpha }{cos \alpha } - \frac{sin \alpha }{cos \alpha } =0 \\ 0=0$