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

Question

The distance between the points $(a \cos α, a \sin α)$ and $(a \cos β, a \sin β)$ is

Smart Achievers · Accepted Answer

(2)

$The points are (a \cos α, a \sin α) and (a \cos β, a \sin β) .$

$So, d = \sqrt{a^{2} {(\cos α - \cos β)}^{2} + a^{2} {(\sin α - \sin β)}^{2}}$

$=$ $| a |$ $| \sqrt{1 + 1 - 2 \cos α \cos β - 2 \sin α \sin β} |$

$=$ $| a |$ $| \sqrt{4 \sin^{2} (\frac{α - β}{2})} |$ $= 2$ $| a \sin (\frac{α - β}{2}) |$

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