Q. If$\ y = 1 + 4\sin^{2}{x\cos^{2}{x,\ }}$ then
A) $1 \leq y \leq 2$
B) $- 1 \leq y \leq 1$
C) $- 3 \leq y \leq 3$
D) None of these
Explanation
(a)
Since, $y = 1 + 4\sin^{2}{x\cos^{2}x}$
$\Rightarrow y = 1 + \sin^{2}{2x}$
We know that, $0 \leq \sin^{2}{2x\ \leq 1}$
$\Rightarrow 1 \leq 1 + \sin^{2}{2x \leq 2}$
$\Rightarrow 1 \leq y \leq 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.