高一三角函数公式讲解视频（人教版高一数学三角函数的所有公式）

1、两角和与差的三角函数cos(α+β)=cosα·cosβ-sinα·sinβ, cos(α-β)=cosα·cosβ+sinα·sinβ, sin(α±β)=sinα·cosβ±cosα·sinβ, tan(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)=(cosα)^2-(sinα)^2=2(cosα)^2-1=1-2(sinα)^2, tan(2α)=2tanα/(1-tan^2α), cot(2α)=(cot^2α-1)/(2cotα), sec(2α)=sec^2α/(1-tan^2α), csc(2α)=1/2*secα·cscα三倍角公式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), cot(3α)=(cot^3α-3cotα)/(3cot^2α-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)/sinα, cot(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^2α=(1-cos(2α))/2=versin(2α)/2, cos^2α=(1+cos(2α))/2=covers(2α)/2,tan^2α=(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·sinγ, cos(α+β+γ)=cosα·cosβ·cosγ-cosα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγ, tan(α+β+γ)=(tanα+tanβ+tanγ-tanα·tanβ·tanγ)/(1-tanα·tanβ-tanβ·tanγ-tanγ·tanα)其它公式1+sin(a)=(sin(a/2)+cos(a/2))^2, 1-sin(a)=(sin(a/2)-cos(a/2))^2, csc(a)=1/sin(a) sec(a)=1/cos(a), cos30°=sin60°, sin30°=cos60°推导公式tanα+cotα=2/sin2α, tanα-cotα=-2cot2α, 1+cos2α=2cos^2α, 1-cos2α=2sin^2α, 1+sinα=[sin(α/2)+cos(α/2)]^2。