Integrals — Class 12 Maths Solution

}

Let $I = \int {\frac{{dx}}{{1 + \cos x}}} = \int {\frac{{dx}}{{1 + 2{{\cos }^2}\frac{x}{2} - 1}}}$

$= \frac{1}{2}\int {\frac{1}{{{{\cos }^2}\frac{x}{2}}}} dx = \frac{1}{2}\int {{{\sec }^2}} \frac{x}{2}dx$

$= \frac{1}{2} \cdot \tan \frac{x}{2} \cdot 2 + C = \tan \frac{x}{2} + C$