What is  the antiderivative (cos2x-cos^2x)^-1 ?

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We have to find the anti-derivative of [ cos 2x - (cos x)^2]^-1

f(x) = [ cos 2x - (cos x)^2]^-1

=> f(x) = [(cos x)^2 - (sin x)^2 - (cos x)^2]^-1

=> f(x) = -(sin x)^-2

=> f(x) = -1 / (cosec x)^2

Int [ -1 / (cosec x)^2...

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We have to find the anti-derivative of [ cos 2x - (cos x)^2]^-1

f(x) = [ cos 2x - (cos x)^2]^-1

=> f(x) = [(cos x)^2 - (sin x)^2 - (cos x)^2]^-1

=> f(x) = -(sin x)^-2

=> f(x) = -1 / (cosec x)^2

Int [ -1 / (cosec x)^2 dx] = cot x + C

The required anti-derivative is cot x + C

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