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[JEE Advanced 2014] For $x\in(0,\pi)$, the equation $\sin x+2\sin2x-\sin3x=3$ has

VAVidaara Admin Asked 1mo ago 1 views 1 answer
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For $x\in(0,\pi)$, the equation $\sin x+2\sin2x-\sin3x=3$ has

(a) infinitely many solutions
(b) three solutions
(c) one solution
(d) no solution

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 1mo ago ▲ 0

Correct answer: (d) no solution

$\sin x-\sin3x=-2\cos2x\sin x$, so LHS $=2\sin x(1-\cos2x)+\,$… its maximum on $(0,\pi)$ is strictly less than $3$; hence no solution.

JEE Advanced 2014 · Trigonometry — verified solution by the Vidaara Team.

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