General solution of equation sin^{100}x,-,cos^{100} x= 1 is

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Trigonometrical Equations

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

A

$2n\pi + \frac{\pi }{3},\,n \in I$

B

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

C

$n\pi + \frac{\pi }{4},\,n \in I$

D

$2n\pi - \frac{\pi }{3},\,n \in I$

Solution

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

Standard 11

Mathematics

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