Question

Ctgx-ctg2x=1/sin2x доказать

Answer 1

$ctgx-ctg2x= \frac{cosx}{sinx} - \frac{cos2x}{sin2x} = \frac{sin2x\cdot cosx-cos2x\cdot sinx}{sinx\cdot sin2x} =\\\\= \frac{sin(2x-x)}{sinx\cdot sin2x} = \frac{sinx}{sinx\cdot sin2x} = \frac{1}{sin2x}$