三角函数有个重要的公式（三角函数的这些公式）

和差公式

sin(A B)=sinAcosB cosAsinB

sin(A-B)=sinAcosB-cosAsinB

cos(A B)=cosAcosB-sinAsinB

cos(A-B)=cosAcosB sinAsinB

tan(A B)=(tanA tanB)/(1-tanAtanB)

tan(A-B)=(tanA-tanB)/(1 tanAtanB)

cot(A B)=(cotAcotB-1)/(cotB cotA)

cot(A-B)=(cotAcotB 1)/(cotB-cotA)

二倍角公式

Sin2A=2SinA·CosA

Cos2A=CosA^2-SinA^2=1-2SinA^2=2CosA^2-1

tan2A=2tanA/1-tanA^2

三倍角公示

tan3a=tana·tan(π/3 a)·tan(π/3-a)

和差化积

sin(a) sin(b)=2sin[(a b)/2]cos[(a-b)/2]

sin(a)-sin(b)=2cos[(a b)/2]sin[(a-b)/2]

cos(a) cos(b)=2cos[(a b)/2]cos[(a-b)/2]

cos(a)-cos(b)=-2sin[(a b)/2]sin[(a-b)/2]

tanA tanB=sin(A B)/cosAcosB

积化和差

sin(a)sin(b)=-1/2*[cos(a b)-cos(a-b)]

cos(a)cos(b)=1/2*[cos(a b) cos(a-b)]

sin(a)cos(b)=1/2*[sin(a b) sin(a-b)]

cos(a)sin(b)=1/2*[sin(a b)-sin(a-b)]

诱导公式

sin(-a)=-sin(a)

cos(-a)=cos(a)

sin(π/2-a)=cos(a)