prove that:

, where a= ax – by and β=ay+bx.

Given:-

Take

LHS

=

We know that, Formula

Thus,

=

=

=

Formula used:- a² + b² + 2ab = (a+b)²

=

=

As given

a= ax–by and β= ay+bx

Thus,

= RHS

So,

Hence Proved