Solution
= Solution
The double-angle identity gives $1+\cos2\theta=2\cos^2\theta$. Therefore
$$
\boxed{\int_0^{\pi/4}\frac{d\theta}{1+\cos2\theta}=\frac12\int_0^{\pi/4}\sec^2\theta\,d\theta=\frac12[\tan\theta]_0^{\pi/4}=\frac12.}
$$
= Solution
The double-angle identity gives $1+\cos2\theta=2\cos^2\theta$. Therefore
$$
\boxed{\int_0^{\pi/4}\frac{d\theta}{1+\cos2\theta}=\frac12\int_0^{\pi/4}\sec^2\theta\,d\theta=\frac12[\tan\theta]_0^{\pi/4}=\frac12.}
$$