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

Explanation

To prove that

\[ \sqrt{\sin^4 x + 4 \cos^2 x} - \sqrt{\cos^4 x + 4 \sin^2 x} = \cos 2x, \]

we will start by simplifying the left-hand side (LHS).

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