Q. The number of values of $x$ in the interval $\lbrack 0,\ 3\pi\rbrack$ satisfying the equation $2\sin^{2}{x + 5\sin{x - 3 = 0}}$ is
A) 6
B) 1
C) 2
D) 4
Explanation
(d)
Given, $2\sin^{2}{x + 5\sin{x - 3 = 0}}$
$\Rightarrow \ \ \left( 2\sin{x - 1} \right)\left( \sin{x + 3} \right) = 0$
$\Rightarrow \ \sin{x = \frac{1}{2}}$ [$\because\sin{x \neq - 3}$]
[image:3_image1.emf]
It is clear from figure that the curve intersect the line at four points in the given interval
Hence, number of solutions are 4
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.