Which of the following pairs(s) of function is(are) identical?
\( \mathrm{P} \)
(a) \( f(x)=\sin \left(\tan ^{-1} x\right), g(x)=\frac{x}{\sqrt{1+x^{2}}} \)
W.
(b) \( f(x)=\operatorname{sgn}\left(\cot ^{-1} x\right), g(x)=\sec ^{2} x-\tan ^{2} x \), where \( \operatorname{sgn} x \) denotes signum function of \( x \).
(c) \( f(x)=e^{\ln \left(\cos ^{-1}\left(\frac{x^{2}-1}{x^{2}+1}\right)\right)}, g(x)=\cos ^{-1}\left(\frac{x^{2}-1}{x^{2}+1}\right) \)
(d) \( f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right), g(x)=2 \tan ^{-1} x \)
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