Question

三角函数和 公式怎么推出来的?就是那种 sinA+sinB=.cosA+cosb=...

Answer 1

sin(A+B)=sinAcosB+cosAsinB

sin(A-B)=sinAcosB-cosAsinB

于是

sinA+sinB

=sin((A+B)/2+(A-B)/2)+sin((A+B)/2-(A-B)/2)

=sin((A+B)/2)cos((A-B)/2)+cos((A+B)/2)sin((A-B)/2)

+sin((A+B)/2)cos((A-B)/2)-cos((A+B)/2)sin((A-B)/2)

=2sin((A+B)/2)cos((A-B)/2)

cosA+cosB的推导方式类似