Question

Find the general solution of the equation $sin7\theta =sin3\theta +sin\theta$

• A.
• B.
• C.
• D.

Answer 1

Answer: (B), (C)

The correct options are
B

C

We will try to simplify the terms using the transformation formula. For that we will take $sin\theta$ to L.H.S.

We do this expecting that we get one $sin3\theta$ after simplifying.

$\Rightarrow sin7\theta -sin\theta =sin3\theta$
$\Rightarrow 2sin3\theta cos4\theta =sin3\theta$
$sin3\theta$ = 0 or $cos4\theta$ = 1/2

$\Rightarrow 3\theta =n\pi or4\theta =2n\pi \pm \frac{\pi }{3}$

$\Rightarrow \theta =\frac{n\pi }{3}or\theta =\frac{n\pi }{2}\pm \frac{\pi }{12}$