Mathematics

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

SOLUTION
$\int {\cfrac{{dx}}{{\tan x + \cot x}}}$
$\int {\cfrac{{dx}}{{\cfrac{{\sin x}}{{\cos x}} + \cfrac{{\cos x}}{{\sin x}}}}}$
$\int {\cfrac{{dx}}{{\cfrac{{{{\sin }^2}x + {{\cos }^2}x}}{{\sin x\cos x}}}}}$
$\int {\cfrac{{dx}}{{\left( {\cfrac{1}{{\sin x\cos x}}} \right)}}}$
$\int {\sin x\cos x\,dx}$
Puting ${\sin x}=t$
$\Rightarrow {\cos x}{dx}={dt}$
$\int {t\,dt}$
$=\cfrac{{{t^2}}}{2} + c$
$=\cfrac{{{{\sin }^2x}}}{2} + c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

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