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The general solution of the equation sin...

The general solution of the equation `sin^(100)x-cos^(100)x=1` is (a)`2npi+pi/3,n in I` (b) n`pi+pi/2,n in I` (c)`npi+pi/4,n in I` (d) `2npi=pi/3,n in I`

A

`2npi+pi/3, n in I`

B

`n pi+pi/2, n in I`

C

`n pi+pi/4, n in I`

D

`2n pi-pi/3, n in I`

Text Solution

Verified by Experts

The correct Answer is:
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.H.S.=1.
Then, `x=n pi+pi/2, n in I`
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