[JEE Advanced 1993] The number of solutions of $\tan x+\sec x=2\cos x$ in $[0,2\pi]$ is
The number of solutions of $\tan x+\sec x=2\cos x$ in $[0,2\pi]$ is
(a) $0$
(b) $1$
(c) $2$
(d) $3$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Correct answer: (c) $2$
$\frac{1+\sin x}{\cos x}=2\cos x\Rightarrow2\sin^2x+\sin x-1=0\Rightarrow\sin x=\frac12$ (or $-1$, rejected as $\cos x=0$). So $x=\frac\pi6,\frac{5\pi}6$ — two solutions.
JEE Advanced 1993 · Trigonometry — verified solution by the Vidaara Team.
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