rachel_z
幼苗
共回答了16个问题采纳率:93.8% 举报
sin(a-b)=sinacosb-cosasinb
用单位圆证明
x^2+y^2=1
A(x1,y1),B(x2,y2),C(x3,y3)
sinA=y1,cosA=x1,sinB=y2,cosB=x2,
k1=tanA=y1/x1,k2=tanB=y2/x2
k=tan(a+b)=(tana+tanb)/(1-tanatanb)
=(y1x2+y2x1)/(x1x2-y1y2)
y3=y1x2+y2x1,x3=x1x2-y1y2
sin(a+b)=y1x2+y2x1
sinacosb+cosasinb=y1x2+x1y2=y1x2+y2x1=sin(a+b)
b=-b
sin(a-b)=sinacos(-b)+cosasin(-b)=sinacosb-cosasinb
证明完毕.
1年前
追问
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