sinα·cosβ=(1/2)*[sin(α+β)+sin(α-β)]
cosα·sinβ=(1/2)*[sin(α+β)-sin(α-β)]
cosα·cosβ=(1/2)*[cos(α+β)+cos(α-β)]
sinα·sinβ=(1/2)*[cos(α+β)-cos(α-β)]
sinα+sinβ=2*[sin(α+β)/2]*[cos(α-β)/2]
sinα-sinβ=2*[cos(α+β)/2]*[sin(α-β)/2]
cosα+cosβ=2*[cos(α+β)/2]*[cos(α-β)/2]
cosα-cosβ=-2*[sin(α+β)/2]*[sin(α-β)/2]
sin(3α)=3sinα-4sin^3α=4sinα·sin(60°+α)sin(60°-α)
cos(3α)=4cos^3α-3cosα=4cosα·cos(60°+α)cos(60°-α)
tan(3α)=(3tanα-tan^3α)/(1-3tan^2α)=tanαtan(π/3+α)tan(π/3-α)
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)