Prove that `sqrt(sin^4x+4cos^2x)-sqrt(cos^4x+4sin^2x)=cos2xdot`

Explanation

`L.H.S. = sqrt(sin^4x+4cos^2x) - sqrt(cos^4x+4sin^2x)`

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

`= sqrt(sin^4x+4-4sin^2x) - sqrt(cos^4x+4-4cos^2x)`

`= sqrt((sin^2x-2)^2) - sqrt((cos^2x-2)^2)`

As, `sin^2x-2 and cos^2x-2` will always be negative,

so, it becomes,

`=(2-sin^2x)-(2-cos^2x) `

`=cos^2x-sin^2x`

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