If \( f(x)=\left(\log _{\cot x} \tan x\right)\left(\log _{\tan x} \...

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If \( f(x)=\left(\log _{\cot x} \tan x\right)\left(\log _{\tan x} \cot x\right)^{-1}+\tan ^{-1} \)
\( \mathrm{P} \) \( \frac{4 x}{4-x^{2}} \), then \( f^{\prime}(2) \) is equal to

W
(A) \( \frac{1}{2} \)
(B) \( -\frac{1}{2} \)
(C) 1
(D) -1
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