If \( I=\int[1+\cot (x-\alpha) \cot (x+\alpha)] d x \), then \( I \) equals
(a) \( \log \left|\f...
If \( I=\int[1+\cot (x-\alpha) \cot (x+\alpha)] d x \), then \( I \) equals
(a) \( \log \left|\frac{\cot x-\cot \alpha}{\cot x+\cot \alpha}\right|+C \)
(b) \( \cot 2 \alpha \log \left|\frac{1-\cot x \tan \alpha}{1+\cot x \tan \alpha}\right|+C \)
(c) \( \operatorname{cosec} 2 \alpha \log \left|\frac{\tan x-\cot \alpha}{\tan x+\cot \alpha}\right|+C \)
(d) \( \log |\tan x|-x \log |\tan \alpha|+C \)
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