SOLUTION: How would I express as a sum or difference 2sin(6u)cos(4u)

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Question 69630: How would I express as a sum or difference 2sin(6u)cos(4u)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

How would I express as a sum or difference

2sin%286u%29cos%284u%29

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You have to know two formulas:

sin%28A%2BB%29=sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29
sin%28A-B%29=sin%28A%29cos%28B%29-cos%28A%29sin%28B%29

Substitute (6u) for A and (4u) for B in both:

sin%286u%2B4u%29=sin%286u%29cos%284u%29%2Bcos%286u%29sin%284u%29
sin%286u-4u%29=sin%286u%29cos%284u%29-cos%286u%29sin%284u%29

Combine terms in the parentheses on the left:

sin%2810u%29=sin%286u%29cos%284u%29%2Bcos%286u%29sin%284u%29
 sin%282u%29=sin%286u%29cos%284u%29-cos%286u%29sin%284u%29

Now add these two equations term by term

       sin%2810u%29=sin%286u%29cos%284u%29%2Bcos%286u%29sin%284u%29
        sin%282u%29=sin%286u%29cos%284u%29-cos%286u%29sin%284u%29
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sin%2810u%29%2Bsin%282u%29=2sin%286u%29cos%284u%29

That's the answer sin%2810u%29%2Bsin%282u%29

Edwin