角和与差的三角函数cos(α+β)=cosα·cosβ-sinα·sinβcos(α-β)=cosα·cosβ+sinα·sinβsin(α±β)=sinα·cosβ±cosα·sinβtan(α+β)=(tanα+tanβ)/(1-tanα·tanβ)tan(α-β)=(tanα-tanβ)/(1+tanα·tanβ)和差化积公式sinα+sinβ=2sin[(α+β)/2]cos[(α-β)/2]sinα-sinβ=2cos[(α+β)/2]sin[(α-β)/2]cosα+cosβ=2cos[(α+β)/2]cos[(α-β)/2]cosα-cosβ=-2sin[(α+β)/2]sin[(α-β)/2]积化和差公式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)]倍角公式sin(2α)=2sinα·cosα=2/(tanα+cotα)cos(2α)=cos^2α-sin^2;α=2cos^2;α-1=1-2sin^2;αtan(2α)=2tanα/(1-tan^2;α)cot(2α)=(cot^2;α-1)/(2cotα)sec(2α)=sec^2;α/(1-tan^2;α)csc(2α)=1/2*secα·cscα三倍角公式sin(3α)=3sinα-4sin^3;α=4sinα·sin(60°+α)sin(60°-α)cos(3α)=4cos^3;α-3cosα=4cosα·cos(60°+α)cos(60°-α)tan(3α)=(3tanα-tan^3;α)/(1-3tan^2;α)=tanαtan(π/3+α)tan(π/3-α)cot(3α)=(cot^3;α-3cotα)/(3cotα-1)n倍角公式sin(nα)=ncos^(n-1)α·sinα-C(n,3)cos^(n-3)α·sin^3α+C(n,5)cos^(n-5)α·sin^5α-…cos(nα)=cos^nα-C(n,2)cos^(n-2)α·sin^2α+C(n,4)cos^(n-4)α·sin^4α-…半角公式sin(α/2)=±√((1-cosα)/2)cos(α/2)=±√((1+cosα)/2)tan(α/2)=±√((1-cosα)/(1+cosα))=sinα/(1+cosα)=(1-cosα)/sinαcot(α/2)=±√((1+cosα)/(1-cosα))=(1+cosα)/sinα=sinα/(1-cosα)sec(α/2)=±√((2secα/(secα+1))csc(α/2)=±√((2secα/(secα-1))辅助角公式Asinα+Bcosα=√(A^2;+B^2;)sin(α+arctan(B/A))Asinα+Bcosα=√(A^2;+B^2;)cos(α-arctan(A/B))万能公式sin(a)=(2tan(a/2))/(1+tan^2;(a/2))cos(a)=(1-tan^2;(a/2))/(1+tan^2;(a/2))tan(a)=(2tan(a/2))/(1-tan^2;(a/2))降幂公式sin^2;α=(1-cos(2α))/2=versin(2α)/2cos^2;α=(1+cos(2α))/2=covers(2α)/2tan^2;α=(1-cos(2α))/(1+cos(2α))三角和的三角函数sin(α+β+γ)=sinα·cosβ·cosγ+cosα·sinβ·cosγ+cosα·cosβ·sinγ-sinα·sinβ·sinγcos(α+β+γ)=cosα·cosβ·cosγ-cosα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγtan(α+β+γ)=(tanα+tanβ+tanγ-tanα·tanβ·tanγ)÷(1-tanα·tanβ-tanβ·tanγ-tanγ·tanα)