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sin^(10)x+cos^(10)x=29/16cos^4 2x...

`sin^(10)x+cos^(10)x=29/16cos^4 2x`

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`sin^(10) x+cos^(10)x=29/16 cos^(4) 2x`
`rArr ((1- cos 2x)/2)^(5) + ((1+cos 2x)/2)^(5) =29/16 cos^(4) 2x`
Let `cos 2x=t`. Then
`((1-t)/2)^(5)+((1+t)/2)^(5) =29/16 t^(4)`
or `24 t^(4)-10 t^(2) -1=0`
or `(2t^(2) -1) (12 t^(2) +1) =0`
or `t^(2) =1/2`
or `cos^(2) 2x=1/2 =(1/sqrt(2))^(2)=("cos" pi/4)^(2)`
or `2x=n pi pm pi/4, n in Z`
or `x= (n pi)/2 pm pi/8, n in Z`
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