Question

if A and B are acute angles such that tan A = 1÷3 and tan B = 1 ÷ 2 and tan (A+ B) = tan A + tan B by 1-tanA×tanB, show that A +B = 45°.

Answer 1

Tan A = 1/3 , Tan B = 1/2

Tan (A + B) = (Tan A + Tan B) / [ 1 - (Tan A * Tan B) ]
Tan (A + B) = (1/3 + 1/2 ) / [ 1 - (1/3 * 1/2) ]
Tan (A + B) = (5/6) / (1 - 1/6)
Tan (A + B) = (5/6) / (5/6)
Tan (A + B) = 1
A + B = Tan ^ -1 ( 1 )
A + B = 45°

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