If  $$x\sin^3\theta+y\cos^3\theta=\sin\theta\cos\theta$$ and  $$x\sin\theta=y\cos\theta$$, then the value of $$x^2 + y^2$$ is:

Given, $$x\sin\theta=y\cos\theta$$

$$\Rightarrow$$  $$y=\frac{x\sin\theta}{\cos\theta\ }$$

$$x\sin^3\theta+y\cos^3\theta=\sin\theta\cos\theta$$

$$\Rightarrow$$  $$x\sin^3\theta+\frac{x\sin\theta\ }{\cos\theta\ }\cos^3\theta=\sin\theta\cos\theta$$

$$\Rightarrow$$  $$x\sin^3\theta+x\sin\theta\ \cos^2\theta=\sin\theta\cos\theta$$

$$\Rightarrow$$  $$x\sin\theta\ \left(\sin^2\theta+\cos^2\theta\right)=\sin\theta\cos\theta$$

$$\Rightarrow$$  $$x\sin\theta\ =\sin\theta\cos\theta$$

$$\Rightarrow$$  $$x=\cos\theta$$

$$\therefore\ $$ $$y=\frac{x\sin\theta}{\cos\theta\ }=\frac{\cos\theta\ \sin\theta}{\cos\theta\ }$$

$$\Rightarrow$$  $$y=\sin\theta\ $$

$$\therefore\ $$ $$x^2+y^2=\cos^2\theta\ +\sin^2\theta=1\ $$

Hence, the correct answer is Option D