If $$x sin^3 θ + y cos^3 θ = sin θ cos θ$$ and x sin θ = y cos θ, sin θ ≠ 0, cos θ ≠ 0, then $$x^2 + y^2$$ is

$$x sin^3 θ $$ = $$ x sin θ \times sin^2 θ $$
$$y cos^3 θ$$ =$$ y cos θ \times cos^2 θ $$
$$x sin^3 θ + y cos^3 θ $$ =$$ (x sin θ \times sin^2 θ) $$ + $$( y cos θ \times cos^2 θ )$$
Since $$x sin θ = y cos θ$$
$$x sin^3 θ + y cos^3 θ$$ = $$x sin θ \times (sin^2 θ +cos^2 θ)$$
$$ sin^2 θ + cos^2 θ =1$$
$$x sin θ \times (sin^2 θ +cos^2 θ) = sin θ cos θ $$
$$x= cos θ $$
$$y=sin θ$$
$$x^2 + y^2 = sin^2 θ +cos^2 θ = 1$$
Hence Option C is the correct answer