The number of distinct solutions of the equation, log 1 2 ⁡ sin ⁡ x = 2 - log 1 2 ⁡ cos…

Solution

${\log }_{1/2}\left|\sin x\right|=2-{\log }_{1/2}\left|\cos x\right|$
${\mathrm{l}\mathrm{o}\mathrm{g}}_{1/2}\left|\sin x\cos x\right|=2$
$\left|\sin x\cos x\right|=\frac{1}{4}$
$\sin 2x=\pm \frac{1}{2}$

Number of solution $=8$ .

Asked in: JEE Main 2020 (09 Jan Shift 1)

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