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  4. The value of 4 sin A cos3 A - 4 cos A sin3 A =

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Q. The value of $ 4 \, \sin \, A \cos^3 \, A - 4 \, \cos \, A \, \sin^3 \, A =$

Trigonometric Functions

Solution:

$4 \, \sin \, A \, \cos^3 \, A - 4 \, \cos \, A \, \sin^3 \, A$
$= 4 \, \cos \, A \, \sin \, A \{ \cos^2 \, A - \sin^2 \, A\}$
$= 2 \{ 2 \, \sin \, A \, \cos \, A\} \cos \, 2 \, A$
$= 2 (\sin \, 2A) (\cos \, 2A) = \sin \, 4A$ .