若a,b,c分别表示三角形ABC内角ABC所对的边长,且(sinA+sinB+sinC)(sinA+sinB-sinC)=3sinAsinB.若三角形面为10根号3,周长20,求边c

问题描述:

若a,b,c分别表示三角形ABC内角ABC所对的边长,且(sinA+sinB+sinC)(sinA+sinB-sinC)=3sinAsinB.若三角形面
为10根号3,周长20,求边c

(sinA+sinB+sinC)(sinA+sinB-sinC)=3sinAsinB(sinA+sinB)²-sin²C=3sinAsinBsin²A+2sinAsinB+sin²B-sin²(A+B)=3sinAsinBsin²A+sin²B-(sinAcosB+cosAsinB)²=sinAsinBsin&sup2...