Question

The value of $x$ in $\left(0, \frac{\pi}{2}\right)$ satifying 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)

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