Question

Помогите решить.
1. 1 / sinα- cosα = sinα + cosα / sin^4α - cos^4α
2. cos(α) / cos(-α) - sin(-α) - sin(-α) / cos(-α) + sinα

Answer 1

$1)\; \frac{sin \alpha +cos \alpha }{sin^4 \alpha -cos^4 \alpha }=\frac{sin\alpha +cos \alpha }{(sin^2 \alpha -cos^2 \alpha )(sin^2 \alpha +cos^2 \alpha )}=\\\\=\frac{sin \alpha +cos \alpha }{(sin \alpha -cos \alpha )(sin \alpha +cos \alpha )\cdot 1}=\frac{1}{sin \alpha -cos \alpha }\\\\\\2)\; \frac{cosa}{cos(-a)-sin(-a)}-\frac{sin(-a)}{cos(-a)+sina}=\frac{cosa}{cosa+sina}-\frac{-sina}{cosa+sina}=\\\\=\frac{cosa+sina}{cosa+sina}=1$