SOLUTION: Prove that each is an identity
sin 3 x = 3 sin x - 4 sin^3 x
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Question 443331: Prove that each is an identity
sin 3 x = 3 sin x - 4 sin^3 x
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Use the sum formula for sine:
} = \sin(2x + x) = \sin(2x)\cos(x) + \sin(x)\cos(2x))
\cos(x)\cos(x) + \sin(x)(\cos^2(x) - \sin^2(x)))
\cos^2(x) + \sin(x)\cos^2(x) - \sin^3(x))
\cos^2(x) - \sin^3(x))
Replace cos^2(x) with 1 - sin^2(x):
(1 - \sin^2(x)) - \sin^3(x))
 - 3\sin^3(x) - \sin^3(x))
 - 4\sin^3(x))
Hence, the statement is an identity.
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