Question

How do you evaluate the equation `cos(arctan(sqrt(3)))`?

Answer 1

`1/2`.

Explanation:

The Definition of `arc tan` function :

`arc tan x=theta , x in RR hArr tantheta=x, theta in (-pi/2,pi/2)`.

We know that, `tan(pi/3)=sqrt3, and, pi/3 in (-pi/2,pi/2)`.

`:. arc tansqrt3=pi/3`.

Consequently, `cos(arc tansqrt3)=cos(pi/3)=1/2`.