Question

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

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{12}$
• C. $\frac{\pi }{8}$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (B)

$\frac{\pi }{12}$

$\sin x\cos x=\frac{1}{4}$

$\Rightarrow 2\sin x\cos x=\frac{1}{2}$
$\Rightarrow \sin 2x=\frac{1}{2}=\sin \left(\frac{\pi }{6}\right)$

$\Rightarrow 2x=n\pi +(-1{)}^n\frac{\pi }{6}$

$\Rightarrow x=\frac{n\pi }{2}+(-1{)}^n\frac{\pi }{12}$
For $xϵ(0,\frac{\pi }{2})$
$x=\frac{\pi }{12}$