证明:a2-b2/c2=sin(A-B)/sinC

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/10 07:12:15
证明:a2-b2/c2=sin(A-B)/sinC证明:a2-b2/c2=sin(A-B)/sinC证明:a2-b2/c2=sin(A-B)/sinC正弦定理a2-b2/c2=(sin^2A-sin^

证明:a2-b2/c2=sin(A-B)/sinC
证明:a2-b2/c2=sin(A-B)/sinC

证明:a2-b2/c2=sin(A-B)/sinC
正弦定理
a2-b2/c2=(sin^2A-sin^2B)/sin^2C
=(sinA-sinB)(sinA+sinB)/sin^2C
=[2sin(A-B)/2*cos(A+B)/2*2sin(A+B)/2*cos(A-B)]/sin^2C
=sin(A-B)*sin(A+B)/sin^2C sin(A+B)=sinC
=sin(A-B)/sinC