Question

Integral of cos2x/cos^2 x×sin^2 x dx

Answer 1

Answer:

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Answer 2

Answer:

The value of integration comes out to be $-cot\theta - tan\theta$

Step-by-step explanation:

Here we know that
$cos 2 \theta = cos^2\theta+sin^2\theta$

So
$\int \frac{cos2\theta} {cos^\theta*sin^2\theta}, d\theta \\\\\int \frac{cos^2\theta-sin^2\theta} {cos^\theta*sin^2\theta}, d\theta \\\\\int\frac{cos^2\theta}{cos^\theta*sin^2\theta} \, d\theta -\int\frac{sin^2\theta}{cos^\theta*sin^2\theta} \, d\theta\\\\\int {cosec^2\theta} \, d\theta - \int{sec^2\theta}\,d\theta$

Hence the value comes out to be $-cot\theta - tan\theta$
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