Question

The distance between the points (1, 0) and (2, cot θ) is ______.

Answer 1

The distance between the points (1, 0) and (2, cot θ) is |cosec θ|.

Explanation:

Distance = `sqrt[(2 - 1)^2 + (cot θ - 0)^2)`

= `sqrt(1 + cot^2θ)` 

Using the identity 1 + cot²θ = cosec²θ gives `sqrt("cosec"^2θ) = |"cosec"  θ|` defined for θ ≠ nπ.