Q. If$\ \tan{x + \cot{x = 2,}}$ then $\sin^{2n}{x + \cos^{2n}{x\ }}$is equal to
A) $2^{n}$
B) $- \frac{1}{2}$
C) $\frac{1}{2}$
D) None of these
Explanation
(d)
Since, $\tan{x + \frac{1}{\tan x} = 2}$
$\Rightarrow \tan{x = 1} \Rightarrow x = \frac{\pi}{4}$
$\therefore\sin{x = \frac{1}{\sqrt{2}}\ and\cos{x = \frac{1}{\sqrt{2}}}}$
Hence, $\sin^{2n}{x + \cos^{2n}{x = \frac{1}{2^{n}} + \frac{1}{2^{n}} = \frac{1}{2^{n - 1}}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.