Prove that the distance of the point `(a cos alpha, a sin alpha)` from the origin is independent of `alpha`

Find the length of perpendicular from the point (a cos alpha, a sin alpha) to the line x cos alpha+y sin alpha=p .

The distance between the points (a cos alpha,a sin alpha) and (a cos beta,a sin beta) where a>0

The distance between the points (a cos alpha,a sin alpha) and (a cos beta,a sin beta) where a> 0

tan theta = (sin alpha-cos alpha) / (sin alpha + cos alpha)

Prove that :2sin^(2)theta+4cos(theta+alpha)sin alpha sin theta+cos2(alpha+theta) is independent of theta.

1. Find the distance between the following points.(i) (a cos alpha, a sin alpha) and (a.cos beta, a sin beta)

Prove that the equation of a line passes through the point (a cos^(3)alpha , a sin^(3)alpha ) and perpendicular to the line x tan alpha+y=a sin alpha is x cos alpha-y sin alpha-a cos 2 alpha .

Perpendicular from the origin to the line joining the points (c cos alpha,c sin alpha) and (c cos beta,c sin beta) divides it in the ratio

Perpendicular from the origin to the line joining the points (c cos alpha,c sin alpha) and (c cos beta,c sin beta) divides it in the ratio