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

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Answer 1 · 2018-03-06T05:50:41

$1/2$ .

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

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