Question

为什么sin(A+C)=sinB得cosB=1/2

Answer 1

sinB=sin（A+C）/2 ∵B=180º-(A+C) ∴B/2=90º-(A+C)/2 ∴sin（A+C）/2=cosB/2 ∵sinB=2sinB/2cosB/2 ∴2sinB/2cosB/2=cosB/2 ∴cosB/2(sinB/2-1/2)=0 ∵0

Answer 2

A+B+C=π
A+C=π-B
sin(A+C)=sin(π-B)
=sinB