Let `A=sinx+cosx`,Then find the value of `sin^4c+cos^4c`in terms of A.

Explanation

`A=sinx+cosx`
`:. A^2=1+2sinxcosx`
Now, `sin^4+cos^4x=(sin^2x+cos^2x)^2-2sin^2xcos^2x`
`=1-2sin^2cos^2x`
`=1-2((A^2-1)/2)^2`
`=1-((A^2-1)^2)/2`
`=(2-(A^4-2A^2+1))/2`
`=(1+2A^2-A^4)/2`
`=1/2+A^2-1/2A^4`