(Acosθ+Bsinθ)^2+(Asinθ-Bcosθ)^2
=A²cos²θ+B²sin²θ+2ABsinθcosθ+A²sin²θ+B²cos²θ-2ABsinθcosθ
=A²cos²θ+B²sin²θ+A²sin²θ+B²cos²θ
=A²+B²