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Which expression correctly equals sin 4A in terms of sin A and cos A?

1. 4*sinA*cos³A - 4*cosA*sin³A
2. 4*sinA*cos³A + 4*cosA*sin³A
3. 2*sinA*cos³A - 2*cosA*sin³A
4. 4*sin³A*cosA - 4*cos³A*sinA

Correct answer: 4*sinA*cos³A - 4*cosA*sin³A

Solution

Expanding sin 4A = 2 sin2A cos2A yields 4 sinA cosA (cos²A - sin²A) = 4 sinA cos³A - 4 cosA sin³A.

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