<s>[INST] Simplify $\sqrt{1-\sin^4x}-\sqrt{1-\cos^4x}$ 
Simplify
$$\sqrt{1-\sin^4x}-\sqrt{1-\cos^4x}$$

My Try
$$A:=\sqrt{1-\sin^4x}-\sqrt{1-\cos^4x}\\A^2=1-\sin^4x-1+\cos^4x-2\sqrt{(1-\sin^4x)(1-\cos^4x)}\\A^2=\cos^4x-\sin^4x-2\sqrt{(\sin x\cos x)^2(1+\sin^2x)(1+\cos^2x)}$$
Now what ?
 [/INST] \begin{align}
\sqrt{1-\sin^{4} x} - \sqrt{1-\cos^{4} x} & = \sqrt{(1-\sin^{2} x)(1+\sin^{2} x)} - \sqrt{(1-\cos^{2} x)(1+\cos^{2} x)} \\
 & = \sqrt{(cos^{2} x)(1+\sin^{2} x)} - \sqrt{(sin^{2} x)(1+\cos^{2} x)} \\ 
 & = \lvert \cos x\rvert\sqrt{1+\sin^{2} x} - \lvert \sin x\rvert\sqrt{1+\cos^{2} x} \\
\end{align}
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