निम्न बिंदुओं के बीच की दूरी ज्ञात कीजिए-
`A(a cos alpha, a sin alpha,), B (a cos beta,a sin beta)`

Explanation

`AB = sqrt((a cos beta - a cos alpha)^(2) + (a sin beta - a sin alpha)^(2))`
` = sqrt(a^(2) ( cos beta -c os alpha)^(2) + a^(2) ( sin beta - sin alpha)^(2))`
` = a sqrt(cos^(2) alpha + cos^(2) beta - 2 cos alpha cos beta + sin^(2) beta + sin^(2) alpha - 2 sin alpha sin beta)`
` = a sqrt((cos^(2) alpha + cos^(2) sin^(2) alpha) + (cos^(2) beta + sin^(2)beta)-2(cos alpha cos beta + sin alpha sin beta))`
` = a sqrt(1+1-2(cos alpha cos beta + sin alpha sin beta))" " [because cos (A-B) = cos A cos B + sin A sin B]`
` = asqrt(2-2cos (alpha-beta))`