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  4. The period of the function f(x)= cos 4 x+ tan 3 x is

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

Trigonometric Functions

Solution:

Let $f(x)=\cos 4 x+\tan 3 x$
Period of $\cos 4 x=\frac{2 \pi}{4}=\frac{\pi}{2} .
$ Period of $\tan 3 x=\frac{\pi}{3}$
$\therefore $ period of $f(x)= LCM$ of $\left(\frac{\pi}{3}, \frac{\pi}{2}\right)=\pi$