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# 高中三角函数公式大全(免费)

tanA ? tanB 1 - tanAtanB

2

Cos2A = Cos2A-Sin2A=2Cos2A-1=1-2sin2A

? 3

? 3

A 2

1 ? cos A 2

1 ? cos A 1 ? cosA

A 2

1 ? cos A 1 ? cosA

1 ? cos A sin A

sin a cos a

a 2 a 1 ? (t an ) 2 2 2 t an
a 1 ? (t an ) 2 2 a 2 1 ? (t an ) 2

cosa= tana=

a 2 a 1 ? (t an ) 2 2 2 t an

b a a b

(a 2 ? b 2 )

×sin(a+c)
(a 2 ? b 2 )

a?sin(a)-b?cos(a) = ×cos(a-c) [其中 tan(c)= ] 2 1+sin(a) =(sin +cos ) 2 1-sin(a) = (sin -cos )
a 2 a 2 a 2 a 2

1 cos a

a

-a

cosh(a)= tg h(a)=

e a ? e -a 2

sinh(a) cosh(a)

? 2
3? 2

3? 2
? 2 ? 2

? 2

? 2

? 2

? 2

? 2

cos（ +α）= sinα tan（ +α）= -cotα cot（ +α）= -tanα sin（ -α）= -cosα cos（ -α）= -sinα tan（ -α）= cotα
3? 2

3? 2

3? 2 3? 2

3? 2

3? 2

cot（ -α）= tanα
3? 2

(以上 k∈Z)

A?sin(ωt+θ)+ B?sin(ωt+φ) =

A 2 ? B 2 ? 2 AB cos( ? ? ? ) ×sin

?t ? arcsin[(As in? ? Bsin? )
A2 ? B 2 ? 2 AB cos(? ? ? )

sin(A+B)=sinAcosB+sinBcosA sin(A-B)=sinAcosB-sinBcosA 这两式相加或相减，可以得到 2 组积化和差: 相加：sinAcosB=[sin(A+B)+sin(A-B)]/2 相减：sinBcosA=[sin(A+B)-sin(A-B)]/2

sin(a+β-β)=msin(a+β+β) sin(a+β)cosβ-cos(a+β)sinβ=msin(a+β)cosβ+mcos(a+β)sinβ sin(a+β)cosβ(1-m)=cos(a+β)sinβ(m+1) tan(α+β)=(1+m)/(1-m)tanβ