Question

The period of the function $\tan (3x+5)$ is

• A. $\frac{2\pi }{3}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{3}$
• D. none of these

Answer 1

Answer: (C)

$\frac{\pi }{3}$

Let, $f\left(x\right)=\tan (3x+5)$
By property of Periodic function.
period of $f\left(x\right)=$ period of $f(x+\lambda ),\lambda ϵR$
$\therefore$ period of $\tan \left(3x\right)=$ period of $\tan (3x+\lambda ),\lambda ϵR$
$\therefore$ period of $\tan (3x+5)=\frac{\pi }{3}$
[Period of $\tan x=\pi ,\therefore$ period of $\tan \lambda x=\frac{\pi }{|\lambda |}andperiodof\tan \left(x\right)=periodof\tan (x+a)$]