Question

Period of $\sin (\frac{\pi }{4}-x)\sin (\frac{\pi }{4}+x)$ is

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

Answer 1

Answer: (B)

$\pi$

Let $f\left(x\right)=sin(\frac{\pi }{4}-x)sin(\frac{\pi }{4}+x)$
$=\frac{cos\left(2x\right)-cos\left(\frac{\pi }{2}\right)}{2}[2sinAsinB=cos(A-B)-cos(A+B\left)\right]$
$f\left(x\right)=\frac{cos2x}{2}[cos\frac{\pi }{2}=0]$
$\therefore$ Period of $f\left(x\right)=\frac{2\pi }{2}=\pi$
[If Period of $f\left(x\right)$ is $T$, then Period of $f\left(kx\right)$ is $\frac{T}{|k|}$]