Equation of a line passing through points (cosθ, sin θ) and (cos Φ, sin Φ). My solution to the above question gives slope of the line(m) as: m= (sinΦ - sinθ)/(cosΦ - cosθ) = -cot(Φ/2 + θ/2) And the equation thereupon is: y = -cot(Φ/2 + θ/2).x + c The value of c comes out to be: c= -cot(Φ/2 + θ/2).cos Φ - sin Φ (on putting in the co-ordinates of second point) Is the expression for 'c' correct? I have some doubts regarding that. Post-Script: _There were no 'Straight-line' tags_

Without checking the trig identities this looks like a mostly correct approach. $$y=mx+c \rightarrow m=\frac{\Delta y}{\Delta x}$$

For finding $c$ few details are provided. I would normally plug in one of the points and solve for $c$. It appears that you may have attempted this?

$$ \sin\Phi = m\cos \Phi+c$$ $$ c = \sin \Phi - m \cos\Phi$$ seems you may have a sign issue with your choice of $c$