Question

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

Answer 1

Substitute the values:tan(A+B)=tanA+tanB1−tanAtanB=12+131−12⋅13=561−16=56÷56=1tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡Atan⁡B=12+131−12⋅13=561−16=56÷56=1Now, since tan(A+B)=1tan⁡(A+B)=1 and tan45∘=1tan⁡45∘=1, then A+B=45∘A+B=45∘

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