Question

(sinA+sinB)(sinA-sinB) = 1/2 sinC^2是怎么化简成为sin(A+B)sin(A-B) = 1/2sin(A+B)^2

Answer 1

(sinA+sinB)(sinA-sinB)=(sinA)^2-(sinB)^2=(sinA)^2-(sinAsinB)^2+(sinAsinB)^2-(sinB)^2=(sinA)^2*[1-(sinB)^2]-(sinB)^2*[1-(sinA)^2]=(sinAcosB)^2-(sinBcosA)^2=(sinAcosB+cosAsinB)*(sinAcosB-cosAsinB)=sin(A+B)sin(A-B)=1/2(sinC)^2=1/2[sin(A+B)]^2
你题目中的sinC^2和sin(A+B)^2应该是表示(sinC)^2和[sin(A+B)]^2吧……
不好意思,有点繁琐,但这种比较简单也容易理解,