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


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