輔助角公式asinα+bcosα=(a2+B2)(1/2)Sin(α+t)，其中Sint = B/(a2+B2)(1/2)cost = A/(a2+B2)(1/2)Tant = B/aasinα+bcosα=(a2+)Tant = A/B冪降公式Sin 2(α)=(1-cos(2α))/2 = versin(25)公式tanα+cotα= 2/sin 2αtanα-cotα=-2 cot 2α1+cos 2α= 2 cos 2α1-cos 2α= 2 sin 2α1+sinα=(sinα/2+cosα/2)。a)+(1-2sin？a)sina =3sina-4sin？a cos3a = cos(2a+a)= cos 2 acosa-sin 2 asina =(2cos？a-1)cosa-2(1-sin？a)cosa =4cos？a-3cosa sin3a=3sina-4sin？a =4sina(3/4-sin？a) =4sina[(√3/2)？罪惡？a] =4sina(sin？60-罪？a)= 4 Sina(sin 60+Sina)(sin 60-Sina)= 4 Sina * 2 sin[(60+a)/2]cos[(60-a)/2]* 2 sin[(60-a)/2]cos[(60-a)/2]= 4 Sina sin(60+a)sin(60-a)cos3a = 4 cos？a-3cosa =4cosa(cos？a-3/4) =4cosa[cos？a-(√3/2)？] =4cosa(cos？a-cos？30)= 4 cosa(cosa+cos 30)(cosa-cos 30)= 4 cosa * 2 cos[(a+30)/2]cos[(a-30)/2]* {-2 sin[(a+30)/2]sin[(a-30)/2]} =-4 cosa sin(a+30)sin(a-30)=-4 cosa sin[90-(60-a)]sin[-90+(60+a)]=-4 cosa cos(60-a)
半角公式Tan(a/2)=(1-COSA)/Sina = Sina/(1+COSA)；cot(a/2)= Sina/(1-COSA)=(1+COSA)/Sina . sin 2(a/2)=(1-COS(a))/2cos 2(a/2)。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？cosγtan(α+β+γ)=(tanα+tanβ+tanγ-tanα？tanβ？tanγ)/(1-tanα？tanβ-tanβ？tanγ-tanγ？Tanα)兩個角的和與差cos(α+β)=cosα？cosβ-sinα？sinβ cos(α-β)=cosα？cosβ+sinα？sinβ sin(α β)=sinα？cosβ cosα？sinβtan(α+β)=(tanα+tanβ)/(1-tanα？tanβ)tan(α-β)=(tanα-tanβ)/(1+tanα？Tanβ)和微分積sinθ+sinφ= 2 sin[(θ+φ)/2]cos[(θ-φ)/2]sinθ-sinφ= 2 cos[(θ+φ)/2]sin[(θ-φ)/2]cosθ+cosφ= 2 cos[cosθ-cosφ=-2 sin[(θ+φ)/2]sin[(θ-φ)/2]tanA+tanB = sin(A+B)/cosAcosB = tan(A+B)(1-tanAtanB)-sin(α-β)]/2歸納公式sin(-α)=-sinαcos(-α)= cosαtan(-a)=-tanαsin(π/2-α)= cosαcos(π/2-α)= sinαsin(π/2+α)= cos。=-sinαsin(π-α)= sinαcos(π-α)=-cosαsin(π+α)=-sinαcos(π+α)=-cosαtanA = sinA/cosA tan(π/2+α)=-cotαtan(π/2-α)= cotαtan(π-α)=-tanαtan(π+α)= tanα。記住竅門:奇偶不變，普適公式sinα= 2tan(α/2)/[1+tan(α/2)]cosα=[1-tan(α/2)]/1+tan(α/2)]tanα= 2。(sinα)^2+(cosα)^2=1(2)1+(tanα)^2=(secα)^2(3)1+(cotα)^2=(cscα)^2