SOLUTION: Given that A and B are acute and Sin A = 4/5, Cos B = 7/25. Find wihout using table the value of tan (A - B).

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Question 754852: Given that A and B are acute and Sin A = 4/5, Cos B = 7/25. Find wihout using table the value of tan (A - B).
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given that A and B are acute and Sin A = 4/5, Cos B = 7/25. Find wihout using table the value of tan (A - B).
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Identity: tan%28A-B%29=%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29+tan%28B%29%29
sinA=4/5
working with a 3-4-5 right triangle in Q1
tanA=opposite side/adjacent side=4/3
..
cosB=7/25
opposite side=√(25^2-7^2)=√576=24
tanB=opposite side/adjacent side=24/7
..
tan%28A-B%29=%284%2F3-24%2F7%29%2F%281%2B4%2F3%2A24%2F7%29
tan%28A-B%29=%2828%2F21-72%2F21%29%2F%281%2B96%2F21%29
tan%28A-B%29=%28-44%2F21%29%2F%28117%2F21%29
tan%28A-B%29=+-44%2F117
..
Check with calculator:
sinA=4/5
A≈53.13º
cosB=7/25
B≈73.74º
A-B≈-20.61º
tan(A-B)=tan(-20.61º)≈-0.3760..
Exact value=-44/117≈-0.3760..