Question

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

• A. $2 \pi$
• B. $\pi$
• C. $\frac{\pi}{2}$
• D. $\frac{3 \pi}{2}$

Answer 1

Answer: (C)

$\frac{\pi}{2}$

Answer 2

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 $\frac{\pi}{2} , \frac{\pi}{2} = \frac{\pi}{2}$