The general solution of the equation sin^ 100 x ,- ,cos^ 100 x= 1… - Vidyadip

MCQ

The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is

A
$2n\pi + \frac{\pi }{3},\,n \in I$
✓
$n\pi + \frac{\pi }{2},\,n \in I$
C
$n\pi + \frac{\pi }{4},\,n \in I$
D
$2n\pi - \frac{\pi }{3},\,n \in I$

✓

Answer

Correct option: B.

$n\pi + \frac{\pi }{2},\,n \in I$

b
We have $\sin ^{100} x-\cos ^{100} x=1$

or $\sin ^{100} x=1+\cos ^{100} x$

Since $L.H.S.\,\, \le 1\,\,and\,\,R.H.S. \ge 1,L.H.S. = R.HS. = 1$

Then, $x=n \pi+\frac{\pi}{2}, n \in I$

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