Question

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

Answer 1

$\frac{1+\sin x}{\cos x(1+cosecx)}$

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

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

$\tan x$

$\text{which has period}2\pi$