Q. If $2\cos^{2}{x + 3\sin{x - 3 = 0,\ 0 \leq x \leq 180{^\circ}}}$, then the value of $x$ is
A) $30{^\circ},90{^\circ},\ 150{^\circ}$
B) $60{^\circ},\ 120{^\circ},\ 180{^\circ}$
C) $0{^\circ},30{^\circ},\ 150{^\circ}$
D) $45{^\circ},\ 90{^\circ},\ 135{^\circ}$
Explanation
(a)
We have, $2\cos^{2}{x + 3\sin{x - 3 = 0}}$
$\Rightarrow 2 - 2\sin^{2}{x + 3\sin{x - 3 = 0}}$
$\Rightarrow (2\sin{x - 1)(\sin{x - 1) = 0}}$
$\Rightarrow \ \sin{x = \frac{1}{2}\ \ or\ \sin{x = 1}}$
$\Rightarrow \ x = 30{^\circ},\ 150{^\circ},\ 90{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.