\( \tan ^{-1}\left[\frac{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}\right]= \...
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0\( \tan ^{-1}\left[\frac{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}\right]= \)
(A) \( \frac{\pi}{4}+\frac{1}{2} \cos ^{-1} x^{2} \)
(B) \( \frac{\pi}{4}+\frac{1}{2} \cos ^{-1} x \)
(C) \( \frac{\pi}{4}+\cos ^{-1} x^{2} \)
(D) \( \frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x^{2} \)
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