Question

The value of $\theta$ satisfying $\sin 7\theta =\sin 4\theta -\sin \theta in0<\theta <\frac{\pi }{2}$ are

• A. $\frac{\pi }{9},\frac{\pi }{4}$
• B. $\frac{\pi }{3},\frac{\pi }{9}$
• C. $\frac{\pi }{6},\frac{\pi }{4}$
• D. $0,1$

Answer 1

The correct option is A $\frac{\pi }{9},\frac{\pi }{4}$

$\sin 7\theta +\sin \theta =\sin 4\theta$

$\Rightarrow 2\sin 4\theta .\cos 3\theta =\sin 4\theta$

$\Rightarrow \sin 4\theta (2\cos 3\theta -1)=0$

$\sin 4\theta =0,\cos 3\theta =\frac{1}{2}$

$\theta =\frac{\pi }{4},\theta =\frac{\pi }{9}$

$\theta =\pi /4,\pi /9$