Question

Find period of $\frac{1+\sin x}{\cos x(1+cosecx)}$.

Answer 1

Let $y=\frac{1+\sin x}{\cos x\left(1+\cos ecx\right)}$

$=\frac{1+\sin x}{\cos x\left(1+\frac{1}{\sin x}\right)}$

$=\frac{\sin x\left(1+\sin x\right)}{\cos x\left(1+\sin x\right)}$

$=\tan x$

Period of $\tan x=\pi$

Period of $y=\pi$