SOLUTION: If sinA=2/3 and CosB=3/5 and . Find Sin(A+B), Cos(A+B), tan(A+B), Where A, B and A+B are positive acute angles

Question 809535: If sinA=2/3 and CosB=3/5 and . Find Sin(A+B), Cos(A+B), tan(A+B), Where A, B and A+B are positive acute angles
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If sinA=2/3 and CosB=3/5 and . Find Sin(A+B), Cos(A+B), tan(A+B), Where A, B and A+B are positive acute angles
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If sin(A) = 2/3, cos(A) = sqrt(5)/3
If cos(B) = 3/5, sin(B) = 4/5
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sin(A+S) = sinA*cosB+cosA*sinB
=(2/3)(3/5)+(sqrt(5)/3)(4/5)
= 6/15 + 4sqrt(5)/25
etc.
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cos(A+B) = cos(A)cos(B)- sin(A)sin(B)
----
= (sqrt(5)/3)*(3/5) - (2/3)(4/5)
====
= (3sqrt(5)/15) - 8/15
----
etc.
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tan(A+B) = sin(A+B)/cos(A+B)
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Cheers,
Stan H.
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