\(\Big(\frac{x}{a}cosθ+\frac{y}{b}sinθ\Big)^2\) + \(\Big(\frac{x}{a}sinθ-\frac{y}{b}cosθ\Big)^2\)=2
\(\frac{x^2}{a^2}cos^2θ+\frac{y^2}{b^2}sin^2θ\) + \(2\frac{xy}{ab}cosθsinθ+\frac{x^2}{a^2}sin^2θ\) + \(\frac{y^2}{b^2}cos^2θ-2\frac{xy}{ab}sinθcosθ=2\)
Hence Proved.