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
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