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  4. What is the period of the function sin 4x + tan 2x?

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Q. What is the period of the function sin 4x + tan 2x?

Relations and Functions - Part 2

Solution:

Period of sin x is $2 \pi $ so, period of
$\sin \, 4x = \frac{2 \pi}{4} = \frac{\pi}{2}$
and period of tan x is $\pi$, so period of
$\tan \, 2x = \frac{\pi}{2}$
So, period of $(\sin \, 4x + \tan \, 2x) $ = LCM of
$\frac{\pi}{2} , \frac{\pi}{2} = \frac{\pi}{2}$