△ABC中,已知sinC+cosC=1-sin(C/2) (1)求sinC (2)若a²+b²=4(a+b)-8,求c边

问题描述:

△ABC中,已知sinC+cosC=1-sin(C/2) (1)求sinC (2)若a²+b²=4(a+b)-8,求c边

(1)sinC+cosC=1-sinC/2,移项得 sinC-sinC/2 = 1-cosC 由二倍角公式得 2sinC/2 cosC/2-sinC/2 = 2(sinC/2)^2 因为sinC/2≠0,所以两边消去sinC/2得 2cosC/2-1 = 2sinC/2 整理得 sinC/2-cosC/2=1/2 根据辅助角公式得s...