sin(α+β)=sinαcosβ+cosαsinβ
sin(α-β)=sinαcosβ-cosαsinβ
cos(α+β)=cosαcosβ-sinαsinβ
cos(α-β)=cosαcosβ+sinαsinβ
tan(α+β)=(tanα+tanβ)/(1-tanα·tanβ)
tan(α-β)=(tanα-tanβ)/(1+tanα·tanβ)
sin2α=2cosαsinα
推导:sin2A=sin(A+A)=sinAcosA+cosAsinA=2sinAcosA
拓展公式:sin2A=2sinAcosA=2tanAcos2A=2tanA/[1+tan2A]
1.Cos2a=Cos2a-Sin2a=[1-tan2a]/[1+tan2a]
推导:cos2A=cos(A+A)=cosAcosA-sinAsinA=cos^2A-sin^2A=2cos^2A-1
tan2α=2tanα/[1-tan2α]
推导:tan2A=tan(A+A)=(tanA+tanA)/(1-tanAtanA)=2tanA/[1-tan2A]
tanA^2=[1-cos2A]/[1+cos2A]
sin2α=sin^2(α+π/4)-cos^2(α+π/4)=2sin^2(a+π/4)-1=1-2cos^2(α+π/4);cos2α=2sin(α+π/4)cos(α+π/4)