Question

If `(cot θ - 1)/(cot θ + 1) = (1 - sqrt(3))/(1 + sqrt(3))` then find the acute angle θ.

Answer 1

`(1 + sqrt(3))(cot θ - 1) = (1 - sqrt(3))(cot θ + 1)`

⇒ `{(1 + sqrt(3)) - (1 - sqrt(3))} cot θ = (1 - sqrt(3)) + (1 + sqrt(3))`

⇒ `2sqrt(3) cot θ = 2`

⇒ `cot θ = 1/sqrt(3)`

⇒ cot θ = cot 60°

⇒ θ = 60°