How to analytically evaluate $\cos(\pi/4+\text{atan}(2))$ This equals $\cos(\pi/4)\cos(\text{atan}(2))-\sin(\pi/4)\sin(\text{atan}(2))$.
I'm just not sure how to evaluate $\cos(\text{atan}(2))$

Graphically, we may say $\theta$ is an angle in a right-angled triangle where the opposite side is 2 and the adjacent side is 1, so that $\arctan{\theta}=2$
As the Hypotenuse side=$\sqrt5$, we have $\cos{(\arctan2)}=\frac{1}{\sqrt5}$

