# How do you evaluate cos(arctan sqrt 3 + arc cot sqrt3) ?

Apr 25, 2016

0

#### Explanation:

If $a = a r c \tan x , \mathmr{and} b + a r c \cot x$, the principal values of a and b are complementary and differ by $\frac{\pi}{2}$. The general values differ by an odd multiple of $\frac{\pi}{2}$.

Anyway, cos ( arc tan x + arc cot x ) = cos ( odd multiple of $\frac{\pi}{2}$ ) = 0.
Here, x = $\sqrt{3}$..