Integral Calculus Question 125
Question: $ \int_{{}}^{{}}{\frac{dx}{\tan x+\cot x}}= $
[MP PET 1991]
Options:
A) $ \frac{\cos 2x}{4}+c $
B) $ \frac{\sin 2x}{4}+c $
C) $ -\frac{\sin 2x}{4}+c $
D) $ -\frac{\cos 2x}{4}+c $
Show Answer
Answer:
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 $ .
BETA
