If tan A=x/x+1 and tan B=1/2x+1 then what does A+B = to?
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tan A + tan B = x/x+1 + 1/2x+1 = (2x^2+2x+1)/(2x^2+3x+1)
tan A tan B = x/ (2x^2+ 3x +1)
1 - tan A tan B = 1 - x/ (2x^2+ 3x +1) = (2x^2+2x+1)/(2x^2+3x+1) = tan A + tan B
tan (A+B) = (tan A + tan B)/ (1- tan A tan B) = 1
SO, A+B = pi/4
tan A tan B = x/ (2x^2+ 3x +1)
1 - tan A tan B = 1 - x/ (2x^2+ 3x +1) = (2x^2+2x+1)/(2x^2+3x+1) = tan A + tan B
tan (A+B) = (tan A + tan B)/ (1- tan A tan B) = 1
SO, A+B = pi/4
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