If x = a cosθ + b sinθ and y = b cosθ - a sinθ, then $$x^2 + y^2$$ is equal to

Expression 1 : $$x=acos\theta+bsin\theta$$

Squaring both sides

=> $$x^2=a^2cos^2\theta+b^2sin^2\theta+2ab(sin\theta)(cos\theta)$$ ------------(i)

Expression 2 : $$y=bcos\theta-asin\theta$$

Squaring both sides,

=> $$y^2=b^2cos^2\theta+a^2sin^2\theta-2ab(sin\theta)(cos\theta)$$ ------------(ii)

Adding equations (i) and (ii), we get :

=> $$x^2+y^2=[a^2cos^2\theta+b^2cos^2\theta+2absin\theta cos\theta]+[a^2sin^2\theta+b^2sin^2\theta-2absin\theta cos\theta]$$

= $$cos^2\theta(a^2+b^2)+sin^2\theta(a^2+b^2)$$

= $$(a^2+b^2)(cos^2\theta+sin^2\theta)$$

= $$a^2+b^2$$

=> Ans - (B)