Q. 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
Explanation
(a)
Given, $\sin{x = 2\sin x\cos x}$
$\Rightarrow \ \sin{x\left( 1 - 2\cos x \right) = 0}$
$\Rightarrow \ \sin{x = 0}$ or $\cos{x = \frac{1}{2}}$
$\Rightarrow \ \ x = 0{^\circ}$ or $x = 60{^\circ},\ - 60{^\circ}$
Hence, number of solution is 3
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.