# Integrate :$\int \large\frac{1}{1+\cos x}$$dx $\begin {array} {1 1} (a)\;\tan \bigg(\frac{x}{2}\bigg)+c \\ (b)\;\sec^2 \bigg(\frac{x}{2}\bigg)+c \\ (c)\;\frac{1}{2}\tan \bigg(\frac{x}{2}\bigg)+c \\ (d)\;2.\tan \bigg(\frac{x}{2}\bigg)+c \end {array}$ ## 1 Answer Using trigonometry property:- 1+ \cos 2 \theta = 2\cos ^2 \theta => \large\frac{1}{2 \cos ^2 x/2} => \large\frac{1}{2}$$\int \sec^2 \bigg(\large\frac{x}{2}\bigg) $$dx => \large\frac{1}{2} \times$$ \tan (\large \frac{x}{2})$$\times 2 +c By solving this we get, \tan \bigg(\large\frac{x}{2}\bigg)+$$c$
Hence a is the correct answer.