Rewrite 6(sin5x)cos2x

Question

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

Answer 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.

 

 

 

Answer 2

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!