小学美术工作思路:三角函数问题:sinA+sinB+sinC=?

来源:百度文库 编辑:中科新闻网 时间:2024/05/14 19:10:02

如果在三角形中有:

sinA + sinB + sinC
= 2*sin[(A+B)/2]*cos[(A-B)/2] + 2*sin(C/2)*cos(C/2)
= 2*cos(C/2)*cos[(A-B)/2] + 2*cos[(A+B)/2]*cos(C/2)
= 2*cos(C/2)*{cos[(A-B)/2] + cos[(A+B)/2]}
= 4*cos(C/2)*cos(A/2)*cos(B/2)

sinA + sinB + sinC
= 2*sin[(A+B)/2]*cos[(A-B)/2] + 2*sin(C/2)*cos(C/2)
= 2*cos(C/2)*cos[(A-B)/2] + 2*cos[(A+B)/2]*cos(C/2)
= 2*cos(C/2)*{cos[(A-B)/2] + cos[(A+B)/2]}
= 4*cos(C/2)*cos(A/2)*cos(B/2)