三角形ABC中角ABC对边分别为abC己知Sin^2C十Sin2CxsinC十COS2C=1且a十b=5 C=根号7 求

因为(sinC)^2 + sin2C*sinC + cos2C = 1
所以(sinC)^2 + 2sinC*cosC*sinC + (1-2(sinC)^2) = 1
即(2cosC - 1) * (sinC)^2 = 0
所以sinC = 0或者cosC = 1/2
因为C是三角形内角,所以sinC > 0,因此只能是cosC = 1/2
所以C = 60度