Question

The period of the function $f\left(x\right)=\left|sin2x\right|+\left|cos8x\right|$ is

• A. $2\pi$
• B. $\pi$
• C. $\frac{2\pi }{3}$
• D. $\frac{\pi }{2}$
• E. $\frac{\pi }{4}$

Answer 1

Answer: (D)

$f(x)=|\sin 2x|+|\cos 8x|$
Time period of $|\sin 2x|=\frac{\pi }{2}$
Time period of $|\cos 8x|=\frac{\pi }{8}$
Now, time period of $f(x)=$ LCM of $\left\{\frac{\pi }{2},\frac{\pi }{8}\right\}$
$=\frac{\pi }{2}$