For x in(0, pi), the equation sin x+2 sin 2 x | vedclass

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Question

$\sin x+2 \sin 2 x-\sin 3 x=3 $

$\sin x\left(1+2 \cos x-3+4 \sin ^2 x\right)=3 $

$\left(4 \sin ^2 x+2 \cos x-2\right)=\frac{3}{\sin x} $

$2-4

Vedclass · Accepted Answer

no solution

Vedclass · Answer

$\sin x+2 \sin 2 x-\sin 3 x=3 $

$\sin x\left(1+2 \cos x-3+4 \sin ^2 xight)=3 $

$\left(4 \sin ^2 x+2 \cos x-2ight)=\frac{3}{\sin x} $

$2-4 \cos ^2 x+2 \cos x=\frac{3}{\sin x} $

$\frac{9}{4}-\left(2 \cos x-\frac{1}{2}ight)^2=\frac{3}{\sin x} $

$	ext { L.H.S. } \leq \frac{9}{4} \quad \quad 	ext { R.H.S. } \geq 3$

No solution.

For $x \in(0, \pi)$, the equation $\sin x+2 \sin 2 x-\sin 3 x=3$ has

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