Question 880607: If A and B are the measures of two first quadrant angles, find the exact value of each function.
7. If sinA=12/13 and cosB=3/5, find cos(A-B).
8. If cosA=12/13 and cosB=12/37, find tan(A-B).
Please help! I've been stuck on this forever!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If A and B are the measures of two first quadrant angles, find the exact value of each function.
7. If sinA=12/13 and cosB=3/5, find cos(A-B).
Note: cos(A-B) = cos(A)cos(B)+sin(A)san(B)
Since sin(A) = 12/13, cos(A) = sqrt(13^2-12^2)/13 = 5/13
Since cos(B) = 3/5, sin(B) = sqrt(5^2-3^2)/5 = 4/5
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Ans: cos(A-B) = (5/13)(3/5)+(12/13)(4/5) = (15+48)/65 = 63/65
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8. If cosA=12/13 and cosB=12/37, find tan(A-B).
Note: tan(A-B) = (tan(A)-tan(B))/(1+tan(A)tan(B))
Since cos(A) = 12/13, tan(A) = sqrt(13^2-12^2)/12 = 5/12
Since cos(B) = 12/37, tan(B) = sqrt(37^2-12^2)/12 = 35/12
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Ans: tan(A-B) = (5/12 - 35/12)/(1-(5/12)(35/12)) = (-20/12)/(-29/24)
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Cheers,
Stan H.
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