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Let A=sinx+cosxdot Then find the value o...

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

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`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`
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