If \( \int \sin ^{-1} x \cos ^{-1} x d x=f^{-1}(x)\left[A x-x f^{-1...

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If \( \int \sin ^{-1} x \cos ^{-1} x d x=f^{-1}(x)\left[A x-x f^{-1}(x)-2 \sqrt{1-x^{2}}\right] \)
\( \mathrm{P} \)
W \( +\frac{\pi}{2} \sqrt{1-x^{2}}+2 x+C \), then
(1) \( f(x)=\sin x \)
(2) \( f(x)=\cos x \)
(3) \( A=\frac{\pi}{4} \)
(4) \( A=\frac{\pi}{2} \)
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