int frac{dx}{cos 2x - cos^2 x} = | vedclass

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(D) We are given the integral $I = \int \frac{dx}{\cos 2x - \cos^2 x}$.Using the trigonometric identity $\cos 2x = 2\cos^2 x - 1$,we substitute this i

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$\cot x + c$

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(D) We are given the integral $I = \int \frac{dx}{\cos 2x - \cos^2 x}$.Using the trigonometric identity $\cos 2x = 2\cos^2 x - 1$,we substitute this into the denominator:$I = \int \frac{dx}{(2\cos^2 x - 1) - \cos^2 x} = \int \frac{dx}{\cos^2 x - 1}$.We know that $\cos^2 x - 1 = - (1 - \cos^2 x) = -\sin^2 x$.Substituting this back into the integral:$I = \int \frac{dx}{-\sin^2 x} = -\int \csc^2 x \, dx$.Since the derivative of $\cot x$ is $-\csc^2 x$,the integral of $-\csc^2 x$ is $\cot x + c$.Therefore,$I = \cot x + c$.

$\int \frac{dx}{\cos 2x - \cos^2 x} = $

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