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
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