Question

The period of the function $f \left(x\right)=\left|sin\,2x\right|+\left|cos\,8x\right|$ is

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

Answer 1

Answer: (D)

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