**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?

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