Question

Write the value of ∫(1 - sin x)/cos² x dx

Answer 1

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

\(= \int \left(\frac 1{\cos^2x} - \frac{\sin x}{\cos^2 x}\right)dx\)

\(= \int \left(\frac 1{\cos^2x} - \frac{\sin x}{\cos x}\times \frac 1{\cos x}\right)dx\)

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

\(= \tan x-\sec x + C\)

Answer 2

Given  that,