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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 (where n `in`I)

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`sin^100x-cos^100x=(sin^50x+cos^50x)(sin^50x-cos^50x)`
`sin^50x+cos^50x<=1-(1)`
`sin^50x-cos^50x>=1-(2)`
adding equation 1 and 2
`2sin^50x=2`
`sinx=pm1`
`sintheta=sinalpha`
`theta=npi+(-1)^nalpha`
...
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