The value of x in left(0, frac{pi}{2}right) s | vedclass

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Question

(D) Given the equation: $(\sin x)(\cos x) = \frac{1}{4}$ Multiply both sides by $2$: $2 \sin x \cos x = \frac{2}{4}$ Using the identity $\sin 2x = 2 \

Vedclass · Accepted Answer

$\frac{\pi}{12}$

Vedclass · Answer

(D) Given the equation: $(\sin x)(\cos x) = \frac{1}{4}$ Multiply both sides by $2$: $2 \sin x \cos x = \frac{2}{4}$ Using the identity $\sin 2x = 2 \sin x \cos x$,we get: $\sin 2x = \frac{1}{2}$ Since $x \in \left(0, \frac{\pi}{2}\right)$,then $2x \in (0, \pi)$. The values of $2x$ for which $\sin 2x = \frac{1}{2}$ are $2x = \frac{\pi}{6}$ and $2x = \frac{5\pi}{6}$. Therefore,$x = \frac{\pi}{12}$ and $x = \frac{5\pi}{12}$. Both values lie in the interval $\left(0, \frac{\pi}{2}\right)$. Comparing with the given options,$\frac{\pi}{12}$ is the correct value.

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

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