${sin}^{2} A {cos}^{2} B - {cos}^{2} A {sin}^{2} B$ simplifies to

{sin}^{2} A + {sin}^{2} B

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{cos}^{2} B + {cos}^{2} A

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{sin}^{2} A - {sin}^{2} B

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{sin}^{2} A - {cos}^{2} B

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Solution

The correct option is B ${sin}^{2} A - {sin}^{2} B$
${sin}^{2} A {cos}^{2} B - {cos}^{2} A {sin}^{2} B = (sin A cos b - cos A sin B) (sin A cos B + cos A sin B)$ $(∵ a^{2} - b^{2} = (a + b) (a - b))$
$= sin (A - B) sin (A + B)$
$= {sin}^{2} A - {sin}^{2} B$

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