If \( y=(\tan x)^{\cot x}+(\cot x)^{\tan x} \), prove that P \( \fr...

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If \( y=(\tan x)^{\cot x}+(\cot x)^{\tan x} \), prove that
P \( \frac{d y}{d x}=(\tan x)^{\cot x} \cdot \operatorname{cosec}^{2} x(1-\log \tan x)+(\cot x)^{\tan x} \cdot \sec ^{2} x[\log (\cot x)-1] \).

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