A) \[\frac{\cos 2x}{4}+c\]
B) \[\frac{\sin 2x}{4}+c\]
C) \[-\frac{\sin 2x}{4}+c\]
D) \[-\frac{\cos 2x}{4}+c\]
Correct Answer: D
Solution :
\[\int_{{}}^{{}}{\frac{dx}{\tan x+\cot x}}=\int_{{}}^{{}}{\frac{dx}{\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}}}\] \[=\frac{1}{2}\int_{{}}^{{}}{2\sin x\cos x\,dx}=\frac{-\cos 2x}{4}+c\].
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