Question

Find the period of the function $\frac{1}{2}\{\frac{\left|\sin x\right|}{\cos x}+\frac{\sin x}{\left|\cos x\right|}\}$,
if it can be written as k$\pi$, then k is

Answer 1

$\frac{\sin x}{\left|\cos x\right|}.$ Period of $N^t=2\pi$ and $\pi i.e.,2\pi$

Similarly period of $\frac{\left|\sin x\right|}{\cos x}$ is L.C.M. of $\pi$ and $2\pi i.e.,2\pi$

Hence the period of $f+g$ is L.C.M.of $2\pi ,2\pi$ i.e., $2\pi$