SOLUTION: Prove the identity: {{{sin(3x) = 3*sin(x) – 4*(sin(x))^3}}} (x is theta)

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Question 138821: Prove the identity: sin%283x%29+=+3%2Asin%28x%29+%96+4%2A%28sin%28x%29%29%5E3 (x is theta)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm only manipulating the left side. I'm not touching the right side. I'm only showing it for comparison.


Start with the given equation


Break up to get


Expand using the sum-difference formulas


Replace with . Replace with .


Factor out


Rearrange the terms


Factor out 2


Replace with


Replace with


Distribute


Combine like terms


Distribute




So we've just proven that



is an identity.