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Q19  Find the following integrals integration of  \int \frac{sec ^2 x }{cosec ^2 x } dx

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Given integral \int \frac{sec ^2 x }{cosec ^2 x } dx;

\int \frac{\frac{1}{\cos^2x}}{\frac{1}{\sin^2 x}}\ dx

= \int \frac{\sin^2 x }{\cos ^2 x } \ dx

=\int \tan^2x \dx

=\int (\sec^2 x-1 )\ dx

=\int \sec^2 x\ dx-\int1 \ dx

= \tan x -x+C, where C is any constant value.

Posted by

Divya Prakash Singh

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