JEE Main 2021 (Online) 25th July Evening ShiftQuestion 1
The number of distinct real roots of $\begin{vmatrix}\sin x&\cos x&\cos x\\\cos x&\sin x&\cos x\\\cos x&\cos x&\sin x\end{vmatrix}=0$ in the interval $-\frac{\pi}{4}\le x\le\frac{\pi}{4}$ is :
Determinant
Solution
Determinant $=(\sin x-\cos x)^2(\sin x+2\cos x)=0$. $\sin x=\cos x\Rightarrow x=\pi/4$ (in range). $\tan x=-2$ gives $x=-\arctan2\approx-63^\circ$, outside $[-45^\circ,45^\circ]$. So exactly 1 root. Option (A).