SOLUTION: Rewrite the product as a sum or difference. 2 sin(9x) cos(2x)

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Question 1204746: Rewrite the product as a sum or difference.
2 sin(9x) cos(2x)
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20061)   (Show Source): You can put this solution on YOUR website!

You are probably more familiar with this more common formula than the 
general product-to-sum and sum-to-product formulas, so I prefer to use 
this more familiar one:







Add the two equations:



The left side is a sum.

Edwin
Answer by ikleyn(52863)   (Show Source): You can put this solution on YOUR website!
.
Rewrite the product as a sum or difference.
2 sin(9x) cos(2x)
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Use a general formula

    sin(a)*cos(b) = ,


which is valid for any angles "a" and "b".


In out case, a = 9x, b = 2x.  Therefore

    2*sin(9x)*cos(2x) = sin(9x-2x) + sin(9x+2x) = sin(7x) + sin(11x).    ANSWER

Solved.

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About these formulas, see your textbook on Trigonometry or the lessons

https://www.algebra.com/algebra/homework/Trigonometry-basics/Compendium-of-Trigonometry-Formulas.lesson

https://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson

https://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas-Examples.lesson

in this site.



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