Perpendicular distance from the origin to the line joining the points `(acos theta, asin theta)(acos phi ,asin phi)` is

Explanation

Equation of a line passes through the points `(a cos theta, a sin theta)` and `(a cos phi, a sin phi)` is
`y-a sin theta=(asinphi-a sin theta)/(a cos phi-a cos theta)(x-a cos theta)`
`=(sin phi-sin theta)/(cos phi-costheta)(x-a cos theta)`
`=(2 cos'(phi+theta)/(2)*sin"(phi-theta)/(2))/(-2sin"(phi+theta)/(2)*sin"(phi-theta)/(2))(x-a cos theta)`
`=-(cos"(theta+phi)/(2))/(sin"(theta+phi)/(2))(x-a cos theta)`
`implies y sin"(theta+phi)/(2)-a sin theta*sin"(theta+phi)/(2)`
`=-x cos"(theta+phi)/(2)+a cos theta cos"(theta+phi)/(2)`
`implies x cos"(theta+phi)/(2)+y sin (theta+phi)/(2)`
`-a[cos theta cos"(theta+phi)/(2)+sintheta sin"(theta+phi)/(2)]=0`
`implies x cos (theta+phi)/(2)+y sin (theta+phi)/(2)-a cos(theta-(theta+phi)/(2))=0`
`implies xcos"(theta+phi)/(2)+y sin"(theta+phi)/(2)-acos"((theta-phi)/(2))=0` .......`(1)`
Length of perpendicular from `(0,0)` to line `(1)`
`=|(0+0-a cos"(theta-phi)/(2))/(sqrt(cos^(2)"(theta+phi)/(2)+sin^(2)"(theta+phi)/(2)))|`
`=a cos"((theta-phi)/(2))`