If x = 8(sinθ + cosθ) and y = 9(sinθ - cosθ), then the value of $$\frac{{{x^2}}}{{{8^2}}} + \frac{{{y^2}}}{{{9^2}}}$$  is:

Solution (By Examveda Team)

$$\eqalign{ & \frac{x}{8} = \sin \theta + \cos \theta ........\left( {\text{i}} \right) \cr & \frac{y}{9} = \sin \theta - \cos \theta ........\left( {{\text{ii}}} \right) \cr & {\text{Square and add equation}}\left( {\text{i}} \right){\text{and}}\left( {{\text{ii}}} \right) \cr & \frac{{{x^2}}}{{{8^2}}} + \frac{{{y^2}}}{{{9^2}}} = {\sin ^2}\theta + {\cos ^2}\theta + 2\sin \theta \cos \theta + {\sin ^2}\theta + {\cos ^2}\theta - 2\sin \theta \cos \theta \cr & \frac{{{x^2}}}{{{8^2}}} + \frac{{{y^2}}}{{{9^2}}} = 2 \cr} $$