Question

The number of solutions of $ \sin x=\sin 2x $ between $ \frac{-\pi }{2} $ and $ \frac{\pi }{2} $ is

• A. $ 3 $
• B. $ 2 $
• C. $ 1 $
• D. $ 0 $

Answer 1

The Correct Option is A

Given, $ \sin x=\sin 2x $
$ \Rightarrow $ $ \sin \,x=2\,\sin x\,\cos x $
$ \Rightarrow $ $ \sin x(1-2\,\cos x)=0 $
$ \Rightarrow $ $ \sin x=0 $ or $ \cos \,x=\frac{1}{2} $
$ \Rightarrow $ $ x={{0}^{o}} $ or $ x={{60}^{o,}}\,-{{60}^{o}} $
Hence, number of solution is 3.