Show that $\arctan a+\arctan(\frac{1}{a})=\frac{\pi}{2}$ $$\arctan a+\arctan\left(\frac 1 a \right)=\frac \pi 2$$
I have the mark scheme in front of me, and I understand where the numbers come from, but I don't understand why they do what they do.
You need this part in to show it:

The markscheme says:

Again, I understand where the numbers come from, but can someone explain to me where the first line comes from, as well as the rest of it? It's a "Hence" question so I have to solve it this way.

Supose $a\neq 0$. It's just a way to remember:$$\tan\left(\arctan a+\arctan\frac{1}{a}\right)=\frac{\tan(\arctan a)+\tan\left(\arctan\frac{1}{a}\right)}{1-\tan(\arctan a)\arctan\left(\frac{1}{a}\right)}=\frac{a+\frac{1}{a}}{1-a\cdot \frac{1}{a}}=+\infty. $$ Moreover, $\arctan(+\infty )=\frac{\pi}{2}$
This proof is not correct (but funny anyway :-) )
