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`

Explanation

`sin^100x - cos^100x = 1`

`=>sin^100x = 1+cos^100x`

Now, maximum value of `sin^100x` can be `1`.

So, above equation will satisfy only when `cos^100x =0.`

`:. sin^100x = 1 and cos^100x = 0` is the only solution for this equation.

Now, `sin^100x = 1`

`=>sin^2x = 1`

`=>sinx = +-1`

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