SOLUTION: verify that one side equals the other only work out one side 2sinxcos^3x+2sin^2xcosx = sin2x

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Question 132365: verify that one side equals the other only work out one side
2sinxcos^3x+2sin^2xcosx = sin2x
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2sinxcos^3x+2sin^2xcosx = sin2x
Factor the left side to get:
2sinxcosx(cos^2x + sin^2x) = sin2x
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But cos^2x + sin^2x = 1, So
(2sinxcosx)*1 = sin2x
But 2sinxcosx = sin2x, So
sin2x = sin2x
===================
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You can't verify the statement as you presented it. That's because, in general,2sin%28x%29cos%5E3%28x%29%2B2sin%5E2%28x%29cos%28x%29+%3C%3E+sin%282x%29

I suspect that you made a typing error when you presented the problem and what you meant was:

2sin%28x%29cos%5E3%28x%29%2Bred%282sin%5E3%28x%29%29cos%28x%29+=+sin%282x%29

In that case, factor out 2sin%28x%29cos%28x%29 on the left.

%282sin%28x%29cos%28x%29%29%28cos%5E2%28x%29%2Bsin%5E2%28x%29%29+=sin%282x%29, but cos%5E2%28x%29%2Bsin%5E2%28x%29=1, so 2sin%28x%29cos%28x%29+=sin%282x%29, which is the standard form of the Double Angle Formula for the sine function. If you need to prove that part, just Google 'Double Angle Formula' and you will find several proofs.