Question

Period of the function $f\left(x\right)=\tan \left(\frac{x}{3}\right)+\sin 2x$ is

• A. $4\pi$
• B. $3\pi$
• C. $5\pi$
• D. $2\pi$

Answer 1

The correct option is B $3\pi$

$f\left(x\right)=\tan \left(\frac{x}{3}\right)+\sin 2x$
Period of $\tan x=\pi$
So, Period of $\tan \left(\frac{x}{3}\right)=3\pi$
Similarly, period of $\sin 2x=\pi$

$\therefore$ Period of $f\left(x\right)=L.C.M(3\pi ,\pi )=3\pi$
Hence, the period of $f\left(x\right)$ is $3\pi .$