Trigonometric Identities Question 278
Question: The general solution of the equation $ {{\sin }^{50}}x-{{\cos }^{50}}x=1 $ is
Options:
A) $ 2n\pi +\frac{\pi }{2} $
B) $ 2n\pi +\frac{\pi }{3} $
C) $ n\pi +\frac{\pi }{2} $
D) $ n\pi +\frac{\pi }{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
We have, $ {{\sin }^{50}}x-{{\cos }^{50}}x=1\Rightarrow {{\sin }^{50}}x=1+{{\cos }^{50}}x $ Since $ {{\sin }^{50}}x\le 1 $ and $ 1+{{\cos }^{50}}x\ge 1 $ . therefore, the two sides are equal only if $ {{\sin }^{50}}x=1=1+{{\cos }^{50}}x $ i.e $ {{\sin }^{50}}x=1 $ and $ {{\cos }^{50}}x=0 $
$ \therefore ,x=2n\pi +\frac{\pi }{2},n\in I $ .
BETA
