Question

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

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{6}$
• D. $\pi$

Answer 1

Answer: (D)

$\pi$

Answer 2

$f(x) = \frac{1}{2}\left( 1 + \cos 6x \right) + \tan 4x.$ The period of cos6x is $\frac{2\pi}{6} = \frac{\pi}{3}$ and the period of $\tan 4x$is $\frac{\pi}{4}$.

Hence the period of $f$is 1.c.m. of $\frac{\pi}{3}$ and $\frac{\pi}{4} = \pi$