Find the principal and general solutions of the equation tan x = √3

Question

Find the principal and general solutions of the following equations:
1. tan x = √3

Answer 1

We know that tanπ/3 =√3

tan(π+π/3)=tanπ/3 = √3

⇒tan4π/3

∴ tanπ3 = tan4π/3 = √3

∴ Principal solutions are π/3,4π/3

If tanx = tanπ/3

∴ General solution: x=nπ+π/3 where n∈z