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  4. The value of 4 sin A cos3 A - 4 cos A sin3 A is equal to

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Q. The value of $4\, sin\, A\, cos^3 \,A - 4\, cos\, A\, sin^3\, A$ is equal to

Trigonometric Functions

Solution:

$4sinA\,cos^{3}A-4cosA\,sin^{3}A$
$= 4sinA \,cosA\left(cos^{2}A - sin^{2}A\right)$
$=2sin2A \,cos2A = sin4A$.