Question

求这道题的具体步骤

Answer 1

公式积化和差:
cosA=cos[(A+B)/2+(A-B)/2], cosB=cos[(A+B)/2-(A-B)/2],
cosA+cosB=2cos(A+B)/2cos(A-B)/2
(sinA/2)^2+(sinB/2)^2+(sinC/2)^2=1-2sinA/2sinB/2sinC/2
左边=1/2(1-cosA)+1/2(1-cosB)+(sinC/2)^2
=1-1/2(cosA+cosB)+(sinC/2)^2
=1-1/2*2cos(A+B)/2cos(A-B)/2+(sinC/2)^2
=1-sinC/2cos(A-B)/2-(sinC/2)^2
=1-sinC/2[cosA/2cosB/2+sinA/2sinB/2]+(sinC/2)^2
=1-sinA/2sinB/2sinC/2-[sinC/2cosA/2cosB/2-sinC/2)^2]
=1-sinA/2sinB/2sinC/2-sinC/2(cosA/2cosB/2-sinC/2)
=1-sinA/2sinB/2sinC/2-sinC/2[cosA/2cosB/2-cos(A+B)/2]
=1-sinA/2sinB/2sinC/2-sinC/2[cosA/2cosB/2-(cosA/2cosB/2-sinA/2sinB/2)]
=1-sinA/2sinB/2sinC/2-sinC/2*sinA/2sinB/2
=1-2sinA/2sinB/2sinC/2
左边=右边
2)(b-c)cotA/2+(c-a)cotB/2+(a-b)cotC/2=0