$$\sin ^ { 2 } A - \cos ^ { 2 } A \cdot \cos 2 A ^ { 2 } B =$$
$\frac{-\cos(A\left(\cos(4BA^{2})+1\right))-\cos(2A)}{2}$
$$\left(\sin(A)-\cos(A\left(\cos(2A^{2}B)\right)^{2})\right)\left(\sin(A)+\cos(A\left(\cos(2A^{2}B)\right)^{2})\right)$$
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$\frac{-\cos(2A\left(\cos(2BA^{2})\right)^{2})-\cos(2A)}{2}$
