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

Question

Find the principal and general solutions of the following equations: cot x = − √3

Answer 1

we have cot x = - √ 3

 ⇒ tan x = - 1 / √ 3

.................(1)

as we know that tan (π - θ) = - tan  θ  and  tan (2π -  θ) = - tan  θ

now from (1) we get
 tan x = tan (5π / 6)  and  tan x = tan (11π / 6)

 ⇒ x = 5π / 6  and   x = 11π / 6

so the principal solutions are x = 5π / 6  and   x = 11π / 6