高一数学--函数倍角公式总结
高一数学--函数倍角公式总结
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)
倍角公式
Sin2A=2SinA?CosA
Cos2A=CosA^2-SinA^2=1-2SinA^2=2CosA^2-1
tan2A=2tanA/1-tanA^2
三倍角公式
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)
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