Question

there are two points- (acosα, asinα) and (acosβ, asinβ). Find the distance between the two points. (Coordinate Geometry)

Answer 1

Distance between the points is
$a(\sqrt{(cos \alpha -cos \beta )^{2}+(sin \alpha -sin \beta )^{2}} )$
$a(\sqrt{(cos^{2} \alpha +sin^{2} \alpha )+(cos^{2} \beta +sin^{2} \beta )-2cos \alpha cos \beta -2sin \alpha sin \beta })$
$a(\sqrt{2(1-cos( \alpha - \beta) ) } )$
Hence distance between them is $2|a(sin(\frac{ \alpha - \beta }{2}))|$.