The two angle sum and difference formula is what is the two angle sum difference formula

cos(α+=cosα·cosβ-sinα·sinβ

cos(α-=cosα·cosβ+sinα·sinβ

sin(α+=sinα·cosβ+cosα·sinβ

sin(α-=sinα·cosβ-cosα·sinβ

tan(α+=(tanα+tanβ)/(1-tanα·tanβ)

tan(α-=(tanα-tanβ)/(1+tanα·tanβ)

Trigonometric functions are a class of functions in mathematics that belong to the transcendental functions of elementary functions. Their essence is a mapping between a set of any angles and a set of variables with a ratio of values.

The usual trigonometric function is defined in a planar Cartesian coordinate system, which defines the entire field of real numbers.

Trigonometric Essence: According to the definition of trigonometric function, the derivation formula is based on the following figure, there is sin = y r; cosθ=x/r；tanθ=y/x； cotθ=x/y。

Sine theorem: In ABC, a sin a = b sin b = c sin c c = 2r. where r is the radius of the circumscribed circle of abc.

Cosine theorem: In ABC, B2 = A2 + C2 - 2AC·COS. where is the angle between edge a and edge c.

Trigonometric formula for the sum and difference of two angles:

cos(α+=cosα·cosβ-sinα·sinβcos(α-=cosα·cosβ+sinα·sinβsin(α±=sinα·cosβ±cosα·sinβtan(α+=(tanα+tanβ)/(1-tanα·tanβ)tan(α-=(tanα-tanβ)/(1+tanα·tanβ)

The two corners and the difference formula are as follows:The sinusoidal formula for the sum of two angles.

sin( sin cos cos sin

cos( cos cos sin sin sin The cosine formula for the difference between the two angles: cos( cos cos return to town sin sin is tangent of the sum of the two angles.

Formula: tan( tan tan ) 1-tan tan ) tangent formula for the difference between the two angles: tan( tan tan ) 1 tan ·tan )

Sine, cosine, tangent formula for double angles:

sin2α＝2sinαcosα

cos2α＝cos^2（α）sin^2（α）2cos^2（α）1＝1－2sin^2（α）

tan2 2tan [1 tan 2 ( ) The formula for sine, cosine, tangent of a half-angle:

sin 2( 2) (1 cos ) 2 cos 2 ( hungry hood 2) ( 1 cos ) 2tan 2 ( 2) (1 cos ) 1 cos ) tan ( 2) (1 cos ) sin (1+cos)

The sine formula for the sum of the two angles: sin( sin cos cos sin sin The sine formula for the difference between the two angles: sin( sin cos cos sin The cosine formula for the sum of the two angles:

cos( cos cos sin sin The cosine formula of the two angles difference opens the cavity: cos( cos cos sin sin sin The tangent formula of the sum of the two angles: tan( tan tan ) 1-tan tan )

The tangent formula for the difference between the two angles: tan ( tan tan ) 1 tan ·tan ).

Postgraduate Mathematics Preparation: The Sum of Two Corners Formula.

1. The trigonometric function of the sum and difference of the two angles is a common segment of the formula:

sin(α+sinαcosβ+cosαsinβ

sin(α-sinαcosβ-cosαsinβ

cos(α+cosαcosβ-sinαsinβ

cos(α-cosαcosβ+sinαsinβ

tan(α+tanα+tanβ)/1-tanαtanβ)

tan(α-tanα-tanβ)/1+tanα·tanβ)

2. Double angle formula:

The sine, cosine, and tangent formulas for the doux angle (powering shrinkage equation).

sin2α=2sinαcosα

cos2α=cos^2(α)sin^2(α)2cos^2(α)1=1-2sin^2(α)

tan2α=2tanα/[1-tan^2(α)

3. Half-width formula:

The sine, cosine, and tangent formulas for the half-angles (the formula for the power reduction grip and leakage only the expansion angle).

sin^2(α/2)=(1-cosα)/2

cos^2(α/2)=(1+cosα)/2

tan^2(α/2)=(1-cosα)/1+cosα)

There is also tan(2)=(1-cos) sin =sin (1+cos).

4. Wan Sou can accompany the formula:

sinα=2tan(α/2)/[1+tan^2(α/2)]

cosα=[1-tan^2(α/2)]/1+tan^2(α/2)]

tanα=2tan(α/2)/[1-tan^2(α/2)]

Universal formula derivation:

Derivation: sin2 =2sin cos =2sin cos (cos 2( )sin 2( )

Because cos2( )sin2( )1).

Then divide the * fraction up and down by cos 2 ( ) to get sin2 = 2tan (1 + tan 2 ( ).

Then replace it with 2.

In the same way, the universal formula for cosine can be derived. The universal formula for tangent can be obtained by sine ratio cosine.

5. Triple angle formula:

Formulas for sine, cosine, and tangent of triple angles:

sin3α=3sinα-4sin^3(α)

cos3α=4cos^3(α)3cosα

tan3α=[3tanα-tan^3(α)1-3tan^2(α)

Derivation of the triple angle formula:

Derivation: tan3 = sin3 cos3

sin2αcosα+cos2αsinα)/cos2αcosα-sin2αsinα)

2sinαcos^2(α)cos^2(α)sinα-sin^3(α)cos^3(α)cosαsin^2(α)2sin^2(α)cosα)

Divide the top and bottom by cos 3 ( ) to obtain:

The formula for the two corners and the difference is:(A + sina cos ten cosa sin.)

a) sina cos -cosa sin.

cosa cos -sina sin.

a) = cosacos +sinasin.

10 )=tana+tan ) 1-tanatan ).

a) = tana tan ) 1 + tanatan ).

The sum (difference) formula includes the sine formula for the sum of two angles, and the cosine formula for the sum of two angles.

The tangent of the sum of the two angles.

Formula. The formula of the sum and difference of the two angles is the basis of the identity deformation of trigonometric functions, and other trigonometric formulas.

All of them are deformed on the basis of this formula.

Tips for applying the two-angle and difference-angle formulas:The trigonometric formula for the sum and difference of two angles can be seen as an induction formula.

When using the trigonometric formula of two angles and difference, special attention should be paid to the relationship between angles and angles, so as to complete the purpose of unifying angles and angles and transforming angles.

Sum of two corners and difference formula:Sine formula. <>

Cosine formula. <>

Tangent formula. <>

The above three formulas are called trigonometric formulas of the sum of two angles (difference).

The sum (difference) formula of two angles includes the sine formula of the sum of two angles, the cosine formula of the sum of two angles, and the tangent formula of the sum of two angles. The formula of the sum and difference of the two angles is the basis of the dust difference or identity deformation of the trigonometric function, and other trigonometric formulas are deformed on the basis of this formula.

Trigonometric formula for the sum and difference of two angles: cos( +cos *cos -sin *sin . cos(α-cosα*cosβ+sinα*sinβ。

The sum (difference) formula includes the sine formula for the sum of two angles, the cosine formula for the sum of two angles, and the tangent formula for the sum of two angles. The common argumentative filial piety formula of the sum and difference of the two angles is the basis of the identity deformation of the three-carry excavation angle function, and other trigonometric formulas are deformed on the basis of this scattering formula.