Mathematics

# Solve $\displaystyle\int {\frac{{dx}}{{\tan x + \cot x}}} =$

##### SOLUTION
$\displaystyle\int \dfrac{dx}{\tan x+ \cot x}$

$=\displaystyle\int \dfrac{dx}{\dfrac{\sin x}{\cos x}+\dfrac{\cos x}{\sin x}}$

$=\displaystyle\int \dfrac{\sin x \cos x}{\sin^{2}x+\cos^{2}x}$

$= \displaystyle\int \sin x \, \cos x \, dx$

$= \displaystyle\int \dfrac{2}{2}\sin x \, \cos x\, dx=\dfrac{1}{2}\int \sin 2x \, dx$

$=-\dfrac{1}{4}\cos 2x+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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