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# Rewrite 6(sin5x)cos2x

This is for my trig class. Thanks for the help!

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
1
Using a Product-to-Sum Identity:

6 sin(5x) cos(2x) = 3 [2 sin((7x+3x)/2) cos((7x-3x)/2)

= 3 sin(7x) + 3 sin(3x)

The reason it's important to do this simplification is that it is MUCH easier to integrate 3 sin(7x) + 3 sin(3x) than the original expression. You'll do this in calculus.

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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Dear Serenity,

I am confused.  I believe 6sin(5x)][cos(2x)] is already as simple as it can be.  I mean I suppose you could rewrite it as

6[sin(5x)][1 - sin2(2x)] (from the double angle formula for cos(2x))

but what would be the point?  Do you have some particular answer for which you are striving?

Sometimes I think the professors and/or textbook authors who make up problems regarding trigonometric identities have way to much time on their hands!