SOLUTION: if tan A = 4/3 and tan B=12/5.find cos (A-B)

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Question 313335: if tan A = 4/3 and tan B=12/5.find cos (A-B)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28A%29=sin%28A%29%2Fcos%28A%29
sin%28A%29=4%2FR
cos%28A%29=3%2FR
sin%5E2%28A%29%2Bcos%5E2%28A%29=1
16%2FR%5E2%2B9%2FR%5E2=1
25%2FR%5E2=1
R%5E2=25
R=5
sin%28A%29=4%2F5
cos%28A%29=3%2F5
Similarly for B,
144%2FR%5E2%2B25%2FR%5E2=1
169%2FR%5E2=1
R=13
sin%28B%29=12%2F13
cos%28B%29=5%2F13
Use the trig identity,
cos%28A-B%29=cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29
cos%28A-B%29=%283%2F5%29%285%2F13%29%2B%284%2F5%29%2812%2F13%29+
cos%28A-B%29=%2815%2F65%29%2B%2848%2F65%29+
cos%28A-B%29=63%2F65