Given x2 + y2 = 2, find the value range of x2-2xy-y2

Given x2 + y2 = 2, find the value range of x2-2xy-y2

A:
x^2+y^2=2
Let x = √ 2cost, y = √ 2sint
x^2-2xy-y^2
=2(cost)^2-4sintcost-2(sint)^2
=2cos2t-2sin2t
=2√2cos(2t+45°)∈[-2√2,2√2]
So: the value range is [- 2 √ 2,2 √ 2]