Question

The fundamental period of $\frac{|\sin x|+|\cos x|}{|\sin x-\cos x|+|\sin x+\cos x|}$ is

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

Answer 1

The correct option is B $\frac{\pi }{2}$

Let $f\left(x\right)=\frac{|\sin x|+|\cos x|}{|\sin x-\cos x|+|\sin x+\cos x|}$
$\therefore f(x+\frac{\pi }{2})=\frac{|\cos x|+|\sin x|}{|\cos x-\sin x|+|\cos x+\sin x|}=\frac{|\sin x|+|\cos x|}{|\sin x-\cos x|+|\sin x+\cos x|}=f\left(x\right)$
Hence period of $f\left(x\right)$ is $\frac{\pi }{2}$