Q. The number of solutions of the equation $1 + \sin{x\sin^{2}{\frac{x}{2} = 0}}$, in $\lbrack - \pi,\ \pi\rbrack$ is
A) Zero
B) One
C) Two
D) Three
Explanation
(a)
Given, $1 + \sin{x\left( \frac{1 - \cos x}{2} \right)} = 0$
$\Rightarrow \ \sin{2x - 2\sin{x = 4}}$
Since, the maximum values of $\sin x$ and $\sin{2x}\$are$\ 1,\$which is not possible for any$\ x$ in $\lbrack - \pi,\ \pi\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.