Question

在△ABC中，求证：（a^2-b^2）/c^2=sin(A-B)/sinC

求用核查化级和激化和差算算，希望能写详细点，我没学，希望多长点知识

Answer 1

a/c=sinA/sinC,b/c=sinB/sinC,
(a^2-b^2）/c^2=(sina)^2-(sinb)^2)/(sinc)^2
(sina)^2=(1-cos2a)/2,(sinb)^2=(1-cos2b)/2
(sina)^2-(sinb)^2=(cos2b-cos2a)/2=sin(a-b)sin(b+a)=sin(a-b)sinc
(a^2-b^2）/c^2=(sina)^2-(sinb)^2)/(sinc)^2=sin(A-B)/sinC

追问

呵，我问的是和差化机！