[JEE Advanced 2001] garbled in source original is a 3 3 determinant set to 0 the number
[Garbled in source — original is a $3\times3$ determinant set to $0$.] The number of distinct real roots of the determinant equation $\begin{vmatrix}\cos x&\sin x&\sin x\\\sin x&\cos x&\sin x\\\sin x&\sin x&\cos x\end{vmatrix}=0$ in $[-\frac\pi4,\frac\pi4]$ is
(a) $0$
(b) $2$
(c) $1$
(d) $3$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (c) $1$
The determinant $=(\cos x-\sin x)^2(\cos x+2\sin x)$; on $[-\frac\pi4,\frac\pi4]$ only $\tan x=-\frac12$ gives a root, so there is exactly $1$.
JEE Advanced 2001 · Trigonometry — verified solution by the Vidaara Team.
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