Q. If $f(x) = \cos^{2}x + \sec^{2}x$, then
A) $f(x) < 1\$
B) $f(x) = 1$
C) $1 < f(x) < 2$
D) $f(x) \geq 2$
Explanation
(d)
$\because\ \ \ AM = \frac{\cos^{2}{x + \sec^{2}x}}{2}$
and GM=$\sqrt{\cos^{2}{x.\sec^{2}{x = 1}}}$
We know that, AM$\geq GM$
$\therefore\ \frac{\cos{\ ^{2}x + \sec^{2}x}}{2} \geq 1$
$\Rightarrow \cos^{2}{x + \sec^{2}{x \geq 2 \Rightarrow f(x) \geq 2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.