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
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