Find all solutions of the equation tan^5 x - 9tan x =0.

Question

The answer is Ak\pi where k is any integer,
the constant A= ??.

Answer 1

tan^5 - 9tan = 0
tan(tan^4-9) = 0
tan(tan^2-3)(tan^2+3) = 0
tan(tan-√3)(tan+√3)(tan^2+9) = 0
so,
tan x = 0 or √3 or -√3

now it should be a cinch