Find the antiderivative of Cosx/Sin2x

We have to find the antiderivative of cos x / sin2x

Solution

To find ∫cos x / sin2x we will express the given function in terms f sin and cos

\(\int \frac{\cos x}{\sin ^{2}x}=\int \frac{1}{sin x}. \frac{\cos x}{\sin x}dx\)

We know that 1/sin x= csc x and cotx/sin x = cot x

\(\int \frac{\cos x}{\sin ^{2}x}=\int \csc x. cot x dx\) \(\int \csc x. cot x dx= -\csc x + c\)

Answer

\(\int \frac{cos x}{sin^{2}x}dx = -csc x + C\)

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