Which of following pairs of functions are identical. (a) \( f(x)=e^{\left(n \sec ^{-1} x\right.}...

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Which of following pairs of functions are identical.
(a) \( f(x)=e^{\left(n \sec ^{-1} x\right.} \) and \( g(x)=\sec ^{-1} \mathrm{x} \)
\( \mathrm{P} \)
(b) \( \mathrm{f}(\mathrm{x})=\tan \left(\tan ^{-1} \mathrm{x}\right) \) and \( \mathrm{g}(\mathrm{x})=\cot \left(\cot ^{-1} \mathrm{x}\right) \)
(c) \( \mathrm{f}(\mathrm{x})=\operatorname{sgn}(\mathrm{x}) \) and \( \mathrm{g}(\mathrm{x})=\operatorname{sgn}(\operatorname{sgn}(\mathrm{x})) \)
(d) \( f(x)=\cot ^{2} x \cdot \cos ^{2} x \) and \( g(x)=\cot ^{2} x-\cos ^{2} x \)
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