Question

Find the principal solution of the following equation:

cot θ = 0

Answer 1

The given equation is cot θ = 0 which is same as

tan θ = ∞

We know that,

tan `π/2` = ∞ and tan (π + θ) = tan θ

∴ `tan (π/2) = tan (π + π/2) = tan ((3π)/2)`

∴  `tan (π/2) = tan ((3π)/2) = ∞`, where,

`0 <  π/2 < 2π  and 0 < (3π)/2 < 2π`

∴ cot θ = 0, i.e., tan θ = ∞ gives

`tan θ = tan (π/2) = tan ((3π)/2)`

∴ `θ = π/2 "and"  θ = (3π)/2`

Hence, the required principal solution are `θ = π/2 "and"  θ = (3π)/2`.