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  4. The period of the function f(x)= cos 2 3 x+ tan 4 x is

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Q. The period of the function $f(x)=\cos ^2 3 x+\tan 4 x$ is

Relations and Functions

Solution:

$f(x)=(1 / 2)(1+\cos 6 x)+\tan 4 x$.
The period of $\cos 6 x$ is $2 \pi / 6=\pi / 3$ and the period of $\tan 4 x$ is $\pi / 4$.
Hence the period of $f$ is l.c.m. of $\pi / 3$ and $\pi / 4=\pi$.