Question

If tan (A-B)=1/7 and tan A=1/2 prove that A+B=pi/4
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Answer 1

tan(A-B)=(tanA-tanB)/(1+tanAtanB)
So 1/7=(1-2tanB)/(2+tanB)
So 2+tanB=7-14tanB
Hence tanB=1/3
Now we calculate tan(A+B) and it is equal to 1
So A+B=45 degrees=pi/4