Question 1204746
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Rewrite the product as a sum or difference.
2 sin(9x) cos(2x)
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<pre>
Use a general formula

    sin(a)*cos(b) = {{{(1/2)*(sin(a-b) + sin(a+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).    <U>ANSWER</U>
</pre>

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.