Mathematics

# Interagte : $\int {\dfrac{{\sec \theta }}{{\sec \theta + \tan \theta }}}$

##### SOLUTION
$\displaystyle \int \dfrac {\sec \theta}{\sec \theta +\tan \theta}d\theta =\displaystyle \int \dfrac {\sec \theta (\sec \theta -\tan \theta)}{(\sec \theta +\tan \theta) (\sec \theta -\tan \theta)}d\theta$

$\displaystyle \int \dfrac {\sec^2 \theta -\sec^2 \theta \tan \theta}{\sec^2 \theta -\tan^2 \theta}d \theta$

$\displaystyle \int \dfrac {\sec^2 \theta -\sec \theta \tan \theta}{1}d\theta$

$\displaystyle \int \sec^2 \theta -\displaystyle \int \sec \theta \tan \theta \ d\theta$
$=\tan \theta -\sec \theta +c$

$\displaystyle \int \dfrac {\sec \theta}{\sec \theta +\tan \theta} d\theta =\tan \theta -\sec \theta +c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

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