1+cos2C=2cos²C
cos2A+cos2B=2cos(A+B)cos(A-B)=2cos(180°-C)cos(A-B)=-2cosCcos(A-B)
1+cos2C-cos2A-cos2B
=2cos²C+2cosCcos(A-B)
=2cosC*[cosC+cos(A-B)]
=2cosC*[cos(A-B)-cos(A+B)]
=2cosC*2sinAsinB
=4cosCsinAsinB
所以4cosCsinAsinB=2根号3sinAsinB
即
2cosC=根号3
cosC=根号3/2
C=30°