12. If $\sec \alpha \sqrt{1+\tan ^{2} \alpha}+\tan \alpha \sqrt{\csc ^{2} \alpha-1}=\tan ^{2} \alpha$, determine the sign of the product $\sin (\cos \alpha) \cdot \cos (\sin \alpha)$.
12. From the condition, we get $\sec \alpha \cdot|\sec \alpha|+\tan \alpha|\cot \alpha|=\tan ^{2} \alpha$, so $\sec \alpha>0, \cot \alpha>0$, $\sin \alpha>0, \cos (\sin \alpha)>0$, then the sign of $\sin (\cos \alpha) \cdot \cos (\sin \alpha)$ is positive.