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.Com
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) (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) ]
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