Question

Solve : $\sin 6\theta +\sin 2\theta =0$

Answer 1

$sin6\theta +sin2\theta =0$

$2sin\frac{6\theta +2\theta }{2}cos\frac{6\theta -2\theta }{2}=0$

$\Rightarrow 2sin4\theta cos2\theta =0$

$\Rightarrow sin4\theta cos2\theta =0$

$sin4\theta =0$

$sin4\theta =sinn\pi$

$4\theta =n\pi$

$\theta =n\pi /4$

$cos2\theta =0$

$cos2\theta =cos\theta$

$2\theta =2n\pi \pm \pi /2$

$\theta =\frac{2n\pi }{2}\pm \pi /4$

$=n\pi \pm \frac{\pi }{4}$