取直角坐标系,作单位圆
取一点A,连接OA,与X轴的夹角为A
取一点B,连接OB,与X轴的夹角为B
OA与OB的夹角即为A-B
A（cosA,sinA),B(cosB,sinB)
OA=(cosA,sinA)
OB=(cosB,sinB)
OA*OB
=|OA||OB|cos(A-B)
=cosAcosB+sinAsinB
|OA|=|OB|=1
cos(A-B)=cosAcosB+sinAsinB
以-B替换B得
cos(A+B)=cosAcosB - sinAsinB
以B+π/2替换B得
cos(A+B+π/2) = cosAcos(B+π/2) - sinAsin(B+π/2)
- sin(A+B) = - cosAsinB - sinAcosB
sin(A+B) = sinAcosB + cosAsinB
tan(A+B)= sin(A+B) / cos(A+B)
= (sinAcosB + cosAsinB) / (cosAcosB - sinAsinB)
= (tanA+tanB) / (1 - tanAtanB) 【分子分母同除以cosAcosB】
