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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 47

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Answer:\tan x- \sec x +c

Hint: You must know about the integral rule of trigonometric functions

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


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

\begin{aligned} &\int \frac{1}{\cos ^{2} x}-\frac{\sin x}{\cos ^{2} x} d x \\ &=\int \sec ^{2} x d x-\int \sec x \cdot \tan x \\ &=\tan x-\sec x+c \quad\left[\because \int \sec ^{2} x d x=\tan x \text { and } \int \sec x \cdot \tan x d x=\sec x+c\right] \end{aligned}     


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