Question

已知α,β均为锐角,且tanα=1/2,tanβ=1/3,求α+β的度数

Answer 1

tan(α+β)=(tana+tanβ)/(1-tanatanβ)
=(1/2+1/3)/(1-1/2*1/3)
=1
α,β均为锐角,0<α+β<180
α+β=45

Answer 2

tanA+tanB=tan(A+B)*（1-tanAtanB)
5/6=tan(A+B)*5/6
tan(A+B)=1
A+B=45度

Answer 3

解
由题设可得
tan(a+b)
=(tana+tanb)/[1-tanatanb)
=(5/6)/(5/6)
=1
即tan(a+b)=1
∴a+b=45º