Q. If$\ \sin{x + cosec\ x = 2,\ }\$then $\sin^{n}{x + cosec^{n}x\ }$is equal to
A) 2
B) $2^{n}$
C) $2^{n - 1}$
D) $2^{n - 2}$
Explanation
(a)
Since, $\sin{x + cosec\ x = 2}$
$\Rightarrow \sin{x + \frac{1}{\sin x} = 2}$
$\Rightarrow \sin^{2}{x - 2\sin{x + 1 = 0}}$
$\Rightarrow \left( \sin{x - 1} \right)^{2} = 0\ \Rightarrow \sin{x = 1}$
Now, $\sin^{n}{x + cosec^{n}x = \sin^{n}{x + \frac{1}{\sin^{n}x}}}$
$= 1 + 1 = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.