Question

The period of the function $ f(x)=|\sin 2x|+|cos 8x| $ 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} $