Question

Find the integration of sec^2 x/ cose^2 x.

Answer 1

$\textbf{Hey there}$!


$\textbf{Solution}$:


$\huge \displaystyle \int \frac{sec ^{2}x }{cosec ^{2} x} \times dx$


$\huge{ Using \: identities} :$


$\huge{sec^{2} x \: = \frac{1}{cos^{2} x}}$


$\huge{cosec ^{2} x \: = \frac{1}{sin ^{2}x } }$


$\huge \displaystyle \int \frac{sin^{2}x }{cos ^{2} x} \times dx$


$\huge \displaystyle \int (sec ^{2}x - 1) \times dx$


$\huge \displaystyle \int sec ^{2}x \times dx - \huge \displaystyle \int 1 \times dx$

$\huge{ Using \: identitie}$


$\huge \displaystyle \int sec x^{2} = tanx$


$\huge{Therefore} :$


$\huge{I = tanx - x + c}$



$\huge{\textbf{#Be Brainly}}$.