Question

The value of $4\sin A{\cos }^{3}A-4\cos A{\sin }^{3}A=$

• A. cos 2A
• B. sin 2A
• C. sin 4A
• D. cos 4 A

Answer 1

Answer: (C)

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