SOLUTION: Rewrite the expression as a sum or difference, then simplify if possible. {{{cos(3theta)sin(theta)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Rewrite the expression as a sum or difference, then simplify if possible. {{{cos(3theta)sin(theta)}}}      Log On


   



Question 1003730: Rewrite the expression as a sum or difference, then simplify if possible.
cos%283theta%29sin%28theta%29

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

cos%283theta%29sin%28theta%29

This is the same as

sin%28theta%29cos%283theta%29

We know that these identities hold:

sin%28theta%2B3theta%29=sin%28theta%29cos%283theta%29%2Bcos%28theta%29sin%283theta%29

sin%28theta-3theta%29=sin%28theta%29cos%283theta%29-cos%28theta%29sin%283theta%29

We add those term by term, the last terms cancel and we get:

sin%28theta%2B3theta%29%2Bsin%28theta-3theta%29=2sin%28theta%29cos%283theta%29

sin%284theta%29%2Bsin%28-theta%29=2sin%28theta%29cos%283theta%29

sin%284theta%29-sin%28theta%29=2sin%28theta%29cos%283theta%29

expr%281%2F2%29%28sin%284theta%29-sin%28theta%29%5E%22%22%29=sin%28theta%29cos%283theta%29

Or, distributing and rearranging:

cos%283theta%29sin%28theta%29=expr%281%2F2%29sin%284theta%29-expr%281%2F2%29sin%28theta%29

Edwin