JEE Main 2022 (Online) 25th July Morning ShiftQuestion 1
The number of solutions of $|\cos x|=\sin x$, such that $-4\pi\le x\le4\pi$ is :
Trigonometric Ratio & Identities
Solution
Concept. $|\cos x|=\sin x$ forces $\sin x\ge0$; then $\tan x=\pm1$. Count per period of $2\pi$. Formulas used. (1) $|\cos x|=\sin x\iff\sin x\ge0$ and $\cos x=\pm\sin x$Step 1 - One period. In $[0,2\pi)$, $\sin x\ge0$ means $x\in[0,\pi]$, and $\tan x=\pm1$ there gives $x=\frac\pi4,\frac{3\pi}4$:Step 2 - Count. $[-4\pi,4\pi]$ is $4$ full periods, and the end points are not solutions ($\sin x=0$ but $|\cos x|=1$). So $4\cdot2=8$. Answer: (C)