Mathematics - Trigonometric Equation Question with Solution | TestHub

$\sin x+2\sin 2x-\sin 3x=3$
$\sin x+4 \sin x\cos x-3\sin x+4{\sin }^{3}x=3$
$\sin x \left[-2+4\cos x+4\left(1-{\cos }^{2}x\right)\right]=3$
$\sin x \left[2-\left(4{\cos }^{2}x-4\cos x+1\right)+1\right]=3$
$\sin x {\left[3-{\left(2\cos x-1\right)}^2\right]}^{ }=3$
$\Rightarrow \sin x=1 and 2\cos x-1=0$
$\Rightarrow x=\frac{\pi }{2} and x=\frac{\pi }{3}$
Which is not possible at same time
Hence, no solution