Find the perpendicular distance from the origin to the line joining the points

The equation of the line joining the points (cosθ,sinθ) and (cosϕ,sinϕ) is given by, 

y−sinθ=cosϕ−cosθsinϕ−sinθ​(x−cosθ)

x(sinϕ−sinθ)+y(cosϕ−cosθ)+cosθsinϕ

−cosθsinθ−sinθcosϕ+sinθcosθ=0 

x(sinθ−sinϕ )+y(cosϕ−cosθ)+sin(ϕ−θ)=0

Therefore, the perpendicular distance (d) of the given line from point (0,0) is

= \( \dfrac{∣sin(ϕ−θ)∣}{\sqrt{2(1-cos(ϕ-θ}))}\)

= \( \dfrac{∣sin(ϕ−θ)∣}{\sqrt{2(2sin^2(\dfrac{ϕ-θ}{2}))}}\)

= \( \dfrac{∣sin(ϕ−θ)∣}{2(2sin^2(\dfrac{ϕ-θ}{2}))}\)

= \( \dfrac{∣sin(ϕ−θ)∣}{2sin(\dfrac{ϕ-θ}{2})}\)