Use inverse functions where needed to find all solutions in

Use inverse functions where needed to find all solutions (in exact form) of the equation in the interval [0, 2 pi) tan^2 x - 2 tan x = 0

Solution

Given interval [0,2pi)

tan²(x)-2tan(x) = 0

tan(x)(tan(x)-2)=0

This implies that either tan(x) = 0 or tan(x)-2=0

tan(x) = 0, gives us x=0 and x = pi

tan(x) = 2 gives us, x=arctan(2) and x=pi+arctan(2)

Therefore, all the solutions are,

x = 0, arctan(2), pi, pi+arctan(2)