QJEEM20Ma295d: JEE Main 2020 Mathematics - Class 12 JEEM20Ma295d Solution: The number of distinct solutions of the equation log 1 2

Step-by-Step Verified Solution

$${\log }_{\frac{1}{2}}\left|\sin x\right|=2-{\log }_{\frac{1}{2}}\left|\cos x\right|$$

$$\Rightarrow$$ $${\log }_{\frac{1}{2}}\left|\sin x\right|$$ + $${\log }_{\frac{1}{2}}\left|\cos x\right|$$ = 2

$$\Rightarrow$$ $${\log }_{\frac{1}{2}}\left(\left|\sin x\cos x\right|\right)$$ = 2

$$\Rightarrow$$ $$\left|\sin x\cos x\right|=\frac{1}{4}$$

$$\Rightarrow$$ sin 2x = $$\pm$$ $$\frac{1}{2}$$

$$\therefore$$ Number of distinct solution = 8