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  4. The number of solutions of sin x= sin 2x between (-π /2) and (π /2) is

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

J & K CETJ & K CET 2008Trigonometric Functions

Solution:

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.