Упростить 1) (1-tg a*tg b)/(tg a+tg b) 2) (1+tg a*tg b)/(tg a-tg b)

Решите задачу:

$1)\; \; \frac{1-tg\alpha \, tg \beta }{tg \alpha +tg \beta }=\frac{1-\frac{sin\alpha }{cos\alpha }\cdot \frac{sin \beta }{cos\beta } }{\frac{sin \alpha }{cos \alpha }+\frac{sin \beta }{cos \beta }}= \frac{cos \alpha \, cos\beta -sin\alpha \, cin \beta \alpha }{sin\alpha \, cos\beta +cos\alpha \, sin\beta }=\\\\=\frac{cos(\alpha +\beta )}{sin(\alpha + \beta )} =ctg( \alpha + \beta )$

$2)\; \; \frac{1+tg \alpha \cdot tg \beta }{tg \alpha -tg \beta }=\frac{1+\frac{sin \alpha }{cos\alpha }\cdot \frac{sin \beta }{cos\beta } }{\frac{sin \alpha }{cos\alpha }-\frac{sin \beta }{cos\beta }}=\frac{cos \alpha \cdot cos\beta +sin \alpha \cdot sin \beta }{sin \alpha \cdot cos \beta -sin \beta \cdot cos \alpha } =\\\\= \frac{cos( \alpha - \beta )}{sin( \alpha - \beta )}=ctg( \alpha - \beta )$