# Class 12 Mathematics Integrals: NCERT Solutions for Question 19

This page focuses on the detailed Integrals question answers for Class 12 Mathematics Integrals, addressing the question: '\begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align}'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 19

## \begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align}

\begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align}

\begin{align} =\int \left(\frac{\frac {1}{Cos^2 x}}{\frac{1}{sin^2 x}}\right) . dx\end{align}

\begin{align} =\int \left(\frac{Sin^2x}{Cos^2x}\right) . dx\end{align}

\begin{align} =\int tan^2 x . dx\end{align}

\begin{align} =\int \left(sec^2x - 1\right) . dx\end{align}

\begin{align} =\int sec^2x . dx - \int 1. dx\end{align}

\begin{align} = tanx - x + C\end{align}