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prove that the length of the perpendicular from the origin to the straight line joining the two points having coordinates ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is a cos { ( alpha + beta)/2}.

Mathematics
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Equation of line passing through ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is y-a sin alpha = (a sinbeta -a sinalpha)/( a cosbeta-a cosalpha) *(x-a cosalpha) y-a sinalpha= (sinbeta -sinalpha)(x-a cosalpha)/(cosbeta -cosalpha) y(cosbeta -cosaplha) -asinalpha (cosbeta -cosalpha) = (sinbeta-sinalpha)(x-acosalpha) y(cos beta-cosalpha) =(sinbeta-sinalpha)x- acosalpha sinbeta+asinalpha cosbeta (sinbeta-sinalpha)x +(cosalpha -cosbeta)y +a(sinalpha cosbeta -sinbeta cosalpha)
|dw:1359027554983:dw|Now, Distance between a line Ax+By+C=0 and point (x1,y1) is
Try to use that formula

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Other answers:

k
A=sinbeta -sinalpha B=cosalpha- cosbeta C=a(sinalpha cosbeta -sinbeta cosalpha) x1=0 y1=0
at the end, i got a(sinalphacosbeta-sinbetacosalpha)/√[2+2cos(alpha+beta)]
asin(alpha-beta)/√[2+2cos(alpha+beta)]

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