Q. The maximum value of $4\sin^{2}{x + 3\cos^{2}x}$ is
A) 4
B) 3
C) 7
D) 5
Explanation
(a)
$4\sin^{2}{x + 3\cos^{2}{x = 4\sin^{2}{x + 3 - 3\sin^{2}x}}}$
$= \sin^{2}{x + 3}$
Maximum value of $\sin x$ is 1 at $x = \frac{\pi}{2}$
Maximum value$= (1)^{2} + 3 = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.