Question

\[\int\frac{1}{1 + \cos 2x} dx\]

Answer 1

\[\int\frac{dx}{1 + \cos \left( 2x \right)} \left[ \therefore 1 + \cos\theta = 2 \cos^2 \left( \frac{\theta}{2} \right) \right]\]

\[ = \int\frac{dx}{2 \cos^2 x}\]

\[ = \frac{1}{2}\int \sec^2 x dx\]

\[ = \frac{1}{2}\tan x + C\]