SOLUTION: How to solve this problem and the steps w/five key points? y = Sin 4x? I'm a beginner can u help?

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Question 257759: How to solve this problem and the steps w/five key points?
y = Sin 4x? I'm a beginner can u help?

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This you really can't solve. You can simplify or graph.
(i) y+=+sin%284x%29
--
Now 4x = 2x + 2x, so we get
(ii) y+=+sin%282x+%2B+2x%29
we have an identity:
sin(A+B) = sinA cosB + sinB cosA
or in our case
(iii) Sin%282x%2B2x%29+=+sin2xcos2x+%2B+cos2xsin2x
But these are the same, so we can write
(Iv) 2sin%282x%29
--
Now 2x = x + x, so we get
(v) y+=+sin%28x+%2B+x%29
we have an identity:
sin(A+B) = sinA cosB + sinB cosA
or in our case
(vi) Sin%28x%2Bx%29+=+sinxcosx+%2B+cosxsinx
But these are the same, so we can write
(vii) 2sin%28x%29
From (iv) and (vii), we get
y+=+4sin%28x%29