Question

докажите тождество
sinα/1-cosα=1+cosα/sinα

Answer 1

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