[kevinkevin]

  So I am working on this one math problem in the back of my text book to keep my mind fresh until school starts and I don't see the way to eliminate certain parts of the equation.  I will do my best to show my work as well as describe the problem.
  The question is about different sound waves and involves tuning forks being struck at different times (not really important). 
  I am given the equation f(t)= Csin(ωt)+Csin(ωt+α).  I'm told to use the sine sum formula to show that,
 f(t)= Asin(ωt)+Bcos(ωt), where A and B are constants that depend on α.  Here is my work and the problem i'm having. 

     f(t)= C[sin(ωt)+sin(ωt)cos(α)+sin(α)cos(ωt)]  (using sine sum formula on given equation)
     
     Now I state that A=cos(α) and B=sin(α)

     With that statement I have the fallowing equation,

     f(t)=C[sin(ωt)+Asin(ωt)+Bcos(ωt)]?? 

     This equation contains the equation with in it i'm suppose to have but contains extra material (the C that must be distributed and the sin(ωt)).  I don't off hand see how to eliminate these to obtain what is desired or if I should have a different starting approach, but some help would be appreciated.  I know it's an easy question and I will probably feel bad once I get the answer.  Thanks! 
   
     
   

[curiouscat]

C[sin(ωt)+Asin(ωt)+Bcos(ωt)]  = Csin(ωt)+C*Asin(ωt)+C*Bcos(ωt)

= (C + C*A)sin(ωt) + C*Bcos(ωt)

=D sin(ωt) + E cos(ωt)

QED

[kevinkevin]

  OK thank you.  My only remaining question is you you eliminate (C+C*A) and C*B to get D and E. 

[curiouscat]

  OK thank you.  My only remaining question is you you eliminate (C+C*A) and C*B to get D and E.

That didn't make sense to me.

[kevinkevin]

  Sorry.  I wrote that as I was walking out the door.  What I meant to say was how do you eliminate (C+C*A) and C*B to get just D and E.     

[curiouscat]

D=C+C*A

E= C*B

[kevinkevin]

  That's what I thought but I was not completely sure if it was ok to do.  We can do that because D and E are equal to equations that depend on alpha right?       

[curiouscat]

  That's what I thought but I was not completely sure if it was ok to do.  We can do that because D and E are equal to equations that depend on alpha right?     

Has to be α and C.

[kevinkevin]

Not B?  B depends on alpha too. B=sin(α)