Number of solutions of the equation `cos^4(2x)+2sin^2(2x) =17(cosx+sinx)^8` , `0 lt x lt 2π` is

Explanation

`cos^4 2x+2sin^2 2x=17(cosx+sinx)^8`

`(cos^2 2x)^2+2(sin^2 2x)=17((cosx+sinx)^2)^4`

`(1-sin^2 2x)^2+2sin^2 2x=17(cos^2x+sin^2x+2sinxcosx)^4`

`1+sin^4 2x-2sin^2 2x+2sin^2 2x=17(1+sin2x)^4`

`1+sin^4 2x=17(1+sin2x)^4`

`1+y^2=1(1+y)^4`

Let` sin2x=y`

`1+y^4=17(1+y)^2(1+y)^2`

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