有a.maths 唔識做

Distance between them

= root [ (acosθ- bcosθ)² (bsinθ- asinθ)² ]

= root { [(a-b) cos θ]² [(b-a) sinθ]² }

= root [ (a-b)² cos² θ (b-a)² sin²θ ]

= root [ (a-b)² cos² θ (a-b)² sin²θ ]

= root [ (a-b)² (cos² θ sin²θ) ]

= root [ (a-b)² ( 1 ) ]

= root (a-b)²

=│a-b│


Notes :
(1) (a-b)² = a² - 2ab b² = b ² - 2ba a² = (b-a)²
(2) root ( a² ) = ( root a )² =│a│,where denotes absolute value of a

│a│= a ,if a≥0 and -a , if a〈 0
in simple, │a│must be positive with magnitude of a

it is also important to state that the answer must be expressed as │a-b│
, otherwise marks will be deducted.
the answer such as root(a-b)² is not acceptable for final answer

我睇完waiwaikeith個答案學倒d野^^
thanks

by using distance formula,
distance between 2 points (x1, y1) and (x2, y2)
= sqrt[(x1-x2)2+(y1-y2)2]
thus, the distance between (acosθ, bsinθ) and (bcosθ, asinθ)
= sqrt[(acosθ-bcosθ)2+(bsinθ-asinθ)2]
= sqrt[cos2θ(a-b)2+sin2θ(b-a)2]
= sqrt[cos2θ(a-b)2+sin2θ(a-b)2] ((a-b)2 = (b-a)2)
= sqrt[(cos2θ+sin2θ)(a-b)2]
= sqrt(a-b)2
= a-b or b-a//
as distance is always larger than 0,
when a is larger than b, then the distance = a-b//
when b is larger than a, then the distance = b-a//

Use distance formula
The distance between=sqrt[(a²-b²)cos²θ+(b²-a²)sin²θ]
=sqrt[a²-b²+(2b²-2a²)sin²θ]
=sqrt[a²-b²-2sin²θ(a²-b²)]
=sqrt[(a²-b²)(1-2sin²θ)]
=sqrt[(a²-b²)cos2θ]