Trigonometric Difference of Two Squares
True or False:
\[ \sin (x +y ) \times \sin (x - y ) = \sin ^2 x - \sin ^2 y \]
Inspiration behind the problem: It is well known that \( (x+y) ( x-y) = x^2 - y^2 \). Does this still work if we apply a trigonometric function, or is that a common misconception?