Question

$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0,$ then$\theta$ equal to

• A. $\frac{n\pi}{4}\text{or}n\pi \pm \frac{\pi}{3}$
• B. $\frac{n\pi}{4}\text{or}n\pi \pm \frac{\pi}{6}$
• C. 0
• D. None of these

Answer 1

Answer: (A)

$\frac{n\pi}{4}\text{or}n\pi \pm \frac{\pi}{3}$

Answer 2

$(\sin 6\theta + \sin 2\theta) + \sin 4\theta = 0 \Rightarrow 2\sin 4\theta\cos 2\theta + \sin 4\theta = 0 \Rightarrow \sin 4\theta(2\cos 2\theta + 1) = 0 \Rightarrow \sin 4\theta = 0$ or $2\cos 2\theta + 1 = 0$

$\sin 4\theta = \sin 0$or $\cos 2\theta = \cos\frac{2\pi}{3}$

$4\theta = n\pi$ or $2\theta = 2n\pi \pm \frac{2\pi}{3}$

$\theta = \frac{n\pi}{4}$ or $\theta = n\pi \pm \frac{\pi}{3}$.