Question

The value of $x$ in $\left(0,\frac{\pi }{2}\right)$ satisfying the equation $\sin x\cos x=\frac{1}{4}$ is

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{8}$
• D. $\frac{\pi }{12}$

Answer 1

Answer: (D)

$2\sin x\cos x=\frac{1}{2}$
$\Rightarrow \sin 2x=\frac{1}{2}=\sin \frac{\pi }{6}$
$\Rightarrow 2x=n\pi +(-1{)}^n\frac{\pi }{6}$
$\Rightarrow x=\frac{n\pi }{2}+(-1{)}^n\frac{\pi }{12}$
For $x\in \left(0,\frac{\pi }{2}\right)$
$\therefore x=\frac{\pi }{12}(\because n=0)$