SOLUTION: Hi, I'm having a little trouble with the following problem. Any help and explanations would be greatly appreciated. Represent cos α sin β in terms of functions of

Algebra ->  Equations -> SOLUTION: Hi, I'm having a little trouble with the following problem. Any help and explanations would be greatly appreciated. Represent cos α sin β in terms of functions of      Log On


   

Question 195762: Hi, I'm having a little trouble with the following problem.
Any help and explanations would be greatly appreciated.
Represent cos α sin β
in terms of functions of (α + β) and (α − β).
Thanks -Nick
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
Identity # 1: sin(A + B) = sin(A)cos(B) + cos(A)sin(B)



Identity # 2: sin(A - B) = sin(A)cos(B) - cos(A)sin(B)



Subtract equations:


sin(A + B) - sin(A - B) = (sin(A)cos(B) - sin(A)cos(B)) + (cos(A)sin(B) -(- cos(A)sin(B)) )


sin(A + B) - sin(A - B) = 2cos(A)sin(B)


1/2[ sin(A + B) - sin(A - B) ] = cos(A)sin(B)



Answer: cos(A)sin(B) = 1/2[ sin(A + B) - sin(A - B) ]