Question

三角形ABC中abc 分别为角ABC的对边,且a=2,c=π/4,COS(B/2)=(2根号5)/5 求三角形面积

Answer 1

COS(B/2)=(2根号5)/5

因为：cos(B/2)=√((1+cosB)/2) =(2根号5)/5

(1+cosB)/2=4/5

1+cosB=8/5

cosB=3/5

又因为：sin²B=1-cos²B=1-(3/5)²=16/25

sinB=4/5

三角形面积:S=1/2acsinB=1/2×2×π/4×4/5=π/5