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

The distance of a point (alpha, beta) from the origin is ....

The distance of a point (alpha, beta) from the origin is ....

The distance between the points ( a cos alpha, a sin alpha ) and ( a cos beta, a sin beta ) is

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

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

Prove that sin ( alpha + 30^(@)) = cos alpha + sin (alpha - 30^(@))

The perpendicular from the origin to the line joining the points A(a cos alpha, a sin alpha) and B(a sin beta, a cos beta) divides AB in the ratio

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