The general solution of sin x - 3sin 2x + sin | vedclass

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Question

(b) $\sin x - 3\sin 2x + \sin 3x = \cos x - 3\cos 2x + \cos 3x$

$ \Rightarrow $$2\sin 2x\cos x - 3\sin 2x - 2\cos 2x\cos x + 3\cos 2x = 0$

$ \Ri

Vedclass · Accepted Answer

$\frac{{n\pi }}{2} + \frac{\pi }{8}$

Vedclass · Answer

(b) $\sin x - 3\sin 2x + \sin 3x = \cos x - 3\cos 2x + \cos 3x$

$ \Rightarrow $$2\sin 2x\cos x - 3\sin 2x - 2\cos 2x\cos x + 3\cos 2x = 0$

$ \Rightarrow $ $\sin 2x(2\cos x - 3) - \cos 2x(2\cos x - 3) = 0$

$ \Rightarrow $$(\sin 2x - \cos 2x)\,\,(2\cos x - 3) = 0 \Rightarrow \sin 2x = \cos 2x$

                                                                   $(\,\because \cos x 
e 3/2)$

$ \Rightarrow $ $2x = 2n\pi \pm \left( {\frac{\pi }{2} - 2x} ight)$

$i.e.,$ $x = \frac{{n\pi }}{2} + \frac{\pi }{8}$.

The general solution of $\sin x - 3\sin 2x + \sin 3x = $ $\cos x - 3\cos 2x + \cos 3x$ is

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