Question

Упростите выражение:
1) sin(a) cos(a) / ctg(a) - 1
2) 1+tg(a) / 1+ctg(a)
3) tg(a) - 1 / ctg(a) - 1
4) ctg(a) + 1 / tg(a) + 1​

Answer 1

$3)\; \; \frac{tga-1}{ctga-1}=\frac{\frac{sina}{cosa}-1}{\frac{cosa}{sina}-1}=\frac{(sina-cosa)\cdot sina}{(cosa-sina)\cdot cosa}=\frac{sina}{-cosa}=-tga\\\\\\4)\; \; \frac{ctga+1}{tga+1}=\frac{\frac{cosa}{sina}+1}{\frac{sina}{cosa}+1}=\frac{(cosa+sina)\cdot cosa}{(sina+cosa)\cdot sina}=\frac{cosa}{sina}=ctga$