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Question

Prove that:

sin 4A = 4 sin A cos3 A - 4 cos A sin3 A

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Solution

LHS = sin 4A

= sin 2.2A

= 2 sin 2A cos 2A

= 2(2 sin A cos A). (cos2Asin2A)

= 4 sin A cos3 A - 4 sin3 A cos A

= RHS.


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