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Write a Value of ∫ 1 − Sin X Cos 2 X D X - Mathematics

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Sum

Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]

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Solution

\[\int\left( \frac{1 - \sin x}{\cos^2 x} \right) dx\]
\[ = \int\left( \frac{1}{\cos^2 x} - \frac{\sin x}{\cos^2 x} \right)dx\]
\[ \int\left( \frac{1}{\cos^2 x} - \frac{\sin x}{\cos x} \times \frac{1}{\cos x} \right) dx\]
\[ = \int\left( \sec^2 x - \sec x \tan x \right) dx\]
\[ = \tan x - \sec x + C\]

Concept: Methods of Integration: Integration by Substitution
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 47 | Page 198
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