Question

The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is

• A. $\frac{\pi}{12}$
• B. $\frac{\pi}{6}$
• C. $\frac{\pi}{2}$
• D. $\pi$

Answer 1

Answer: (D)

$\pi$

Answer 2

We have, $f(x)=\cos 4 x+\tan 3 x$
Clearly, period of $\cos 4 x$ is $\frac{2 \pi}{4}=\frac{\pi}{2}$ and that of $\tan 3 x$ is $\frac{\pi}{3}$
$\therefore$ Period of $f(x)=\frac{\operatorname{LCM} \text { of }(\pi \text { and } \pi)}{H C F \text { of }(2 \text { and } 3)}$
$=\frac{\pi}{1}=\pi$