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

Options:

• A: $0$
• B: $1$
• C: $\sin^2 \theta$
• D: $\cos^2 \theta$

Related Practice Questions:

• Which of the following artifacts, extensively found at Burzahom and Gufkral, specifically indicates that the Neolithic inhabitants of Kashmir practiced sewing animal skins for clothing to survive the harsh winters?
• The earliest known evidence of rock art in India, in the form of 'Cupules' (hemispherical cup-shaped depressions carved into rock), belongs to the Lower Paleolithic age and was found at:
• The first human colonization of the fertile Ganga plains, as evidenced by archaeological discoveries at Sarai Nahar Rai and Mahadaha, took place during which period?
• Which prehistoric site located in the Thar Desert of Rajasthan provides a continuous and undisturbed profile of Lower, Middle, and Upper Paleolithic cultures?