Question

How do you evaluate tan (2Pi/3) + tan (Pi/4)?

Answer 1

`tan((2pi)/3)+tan(pi/4)=color(blue)(1-sqrt(3))`

Explanation:

The angles `(2pi)/3` and `pi/4` are two of the "standard angles" for which you should be familiar with their ratios. (See images below).

`tan((2pi)/3)=sqrt(3)/(-1)=-sqrt(3)`

`tan(pi/4)=1/1=1`

`tan((2p)/3)+tan(pi/4) = -sqrt(3)+1 = 1-sqrt(3)`