Question

Find the principal solution of the following equation :

cot θ = `sqrt(3)`

Answer 1

The given equation is cot θ = `sqrt(3)` which is same as tan θ = `1/sqrt(3)`.

We know that,

tan `π/6 = 1/sqrt(3)` and tan(π + θ) = tan θ

∴ `tan  π/6 = tan(π + π/6) = tan  (7π)/(6)`

∴ `tan  π/6 = tan  (7π)/6 = 1/sqrt(3)`, where

`0 < π/6 < 2π and 0 < (7π)/6 < 2π`

∴ cot θ = `sqrt(3)`, i.e. tan θ = `1/sqrt(3)` gives

tan θ = `tan  π/6 = tan  (7π)/6`

∴ θ = `π/6 and θ = (7π)/6`

Hence, the required principal solutions are θ = `π/6 and θ = (7π)/6`.