1.

Let `A=sinx+cosxdot`Then find the value of `sin^4x+cos^4x`in terms of `Adot`

Answer» `A=sinx+cosx`
`A^2=sin^2x+cos^2x+2sinxcosx`
`A^2=(A^2/2-1)`
`sin^4x+cos^4x=(sin^2x)^2+(cos^2x)^2`
`=(sin^2x+cos^2x)^2-2sin^2xcos^2x`
`=1-2(sinxcosx)^2`
`=1-2*(A^2-1)^2/4`
`=(2-(A^2-1)^2)/2`.


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