Question

If sin $3\theta =sin\theta$,then the general value of $\theta$ is

• A. $2n\pi ,(2n+1)\frac{\pi }{3}$
• B. $n\pi ,(2n+1)\frac{\pi }{4}$
• C. $n\pi ,(2n+1)\frac{\pi }{3}$
• D. None of these

Answer 1

Answer: (B)

$n\pi ,(2n+1)\frac{\pi }{4}$

$\sin 3\theta =\sin \theta$

$\Rightarrow 3\theta =m\pi +{(-1)}^m\theta$

$\Rightarrow$ For $\left(m\right)$ even i.e, $m=2n$ then $\theta =\frac{2n\pi }{2}=n\pi$

For $\left(m\right)$ odd i.e, $m=2n+1$ then $\theta =(2n+1)\frac{\pi }{4}.$

Hence, the answer is $n\pi ,(2n+1)\frac{\pi }{4}.$