问题
填空题
a,b,c分别为角A,B,C的对边,S为△ABC的面积,且S=c2-(a-b)2,则tanC=______.
答案
由余弦定理得S=c2-(a2+b2)+2ab=-2abcosC+2ab=2ab(1-cosC)=
absinC,1 2
∴
=1-cosC sinC
,∴1 4
=2sin2 C 2 2sin
cosC 2 C 2
,∴tan1 4
=C 2
,1 4
∴tanC=
=2tan C 2 1-tan2 C 2
=2× 1 4 1-(
)21 4
.8 15
故答案
.8 15