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)

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