解:
(1)由韦达定理可得:
tanα+tanβ=3
tanα*tanβ=-2
tan(α+β)=(tanα+tanβ)/(1-tanα*tanβ)=3/(1-(-2))=1
(2)
(1+tan22°)(1+tan23°)
=1+(tan22°+tan23°)+tan22° * tan23°(a)
然后我们考察:
tan45°=tan(23°+22°)=(tan22°+tan23°)/(1-tan22° * tan23°) =1
--> tan22°+tan23°=1-tan22° * tan23°
--> tan22°+tan23°+tan22° * tan23°=1
--> (a)=1+1=2
也就是:(1+tan22°)(1+tan23°)=2
希望能帮助你哈