Exam

JEE Main

Year

2020

Date

9 January

Shift

Morning Shift

Subject

Mathematics

Chapter

Basics of Mathematics

JEE Main 2020 · 9 January · Morning Shift · Mathematics · Basics of Mathematics

The number of distinct solutions of the equation, _ (1)/(2) | x| =2...

The number of distinct solutions of the equation, $\log_{\dfrac{1}{2}} \left|\sin x\right| =2 - \log_{\dfrac{1}{2}} \left|\cos x\right|$ in the interval \left[0, 2\pi\right], is ________

Step-by-step solution

\log_{1/2} \left|\sin x\right| = 2 - \log_{1/2} \left|\cos x\right|$<br/>$\log_{1/2}\left|\sin x \cos x\right| = 2$<br/>\left|\sin x \cos x\right| = \dfrac{1}{4}$
$\sin 2x = \pm \dfrac{1}{2}$

Number of solution $= 8$ .