已知△ABC的三内角A、B、C同时满足:①2cos²A/2-3cosA=0,②sin²B/2+sin²C/2=1/2试判断△ABC的形状.

问题描述:

已知△ABC的三内角A、B、C同时满足:①2cos²A/2-3cosA=0,②sin²B/2+sin²C/2=1/2
试判断△ABC的形状.

2cos²A/2 -1 = cosA1即cosA +1 -3cosA =0cosA = 1/2A = 60°2即-2sin²B/2 -2sin²C/2 = -2 *1/2 = -11-2sin²B/2 +1-2sin²C/2 = -1 +2cosB + cosC = 12cos(B/2+C/2)cos(B/2-C/2) = 12cos((18...