For α ∈ 0 , π 2 , the angle between the lines represented by x cos θ - y cos θ + tan α x - 1 - cos θ · tan α y = 0 is

Step-by-step solution

Given, x cos θ - y cos θ + tan α x - 1 - cos θ · tan α y = 0 Now taking line L 1 → x cos θ - y = 0 And L 2 → cos θ + tan α x - 1 - cos θ · tan α y = 0 Now slope of line L 1 is m 1 = cos θ and slope of line L 2 is m 2 = cos θ + tan α 1 - cos θ . tan α Now we know that angle between two line is given by tan ϕ = m 2 - m 1 1 + m 1 m 2 ⇒ tan φ = cos θ + tan α 1 - cos θ . tan α - cos θ