If \( \int \frac{\cos 4 x+1}{\cot x-\tan x} d x=A \cos 4 x+B \); where \( A \& B \) are constant...

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If \( \int \frac{\cos 4 x+1}{\cot x-\tan x} d x=A \cos 4 x+B \); where \( A \& B \) are constants, then
(A) \( A=-1 / 4 \) \& \( B \) may have any value
(B) \( A=-1 / 8 \) \& \( B \) may have any value
(C) \( A=-1 / 2 \& B=-1 / 4 \)
(D) \( A=B=1 / 2 \)
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