What is the derivation process of the sum and difference of the two angles of a trigonometric functi

As a unit circle, as 0, , the terminal edge of the angle, and the coordinates of the intersection point of the terminal edge and the unit circle are a(1，0）b（cosα,sinα)

c(cosβ,sinβ),d(cos(α-sin(α-

Connect AD, BCAD=BC

ad)^2=[cos(α-1]^2+[sin(α-0]^2=2-cos(α-bc)^2=(cosα-cosβ)^2+(sinα-sinβ)^2=2-cosαcosβ-sinαsinβ

cos(α-=cosαcosβ+sinαsinβ

sin(α-=cos[π/2-(α=cos[(π/2-α)=cos(π/2-α)cosβ-sin(π/2-α)sinβ

sinαcosβ-cosαsinβ

sin(α+=sinαcosβ+cosαsinβ

The formula for the sum difference between the two angles is derived: sina+sinb=sin[(a+b) 2+(a-b) 2]+sin[(a+b) 2-(a-b) 2]=(sinxcosy+cosxsiny)+(sinxcosy-cosxsiny)=2sin[(a+b) 2]cos[(a-b) 2].

The two-angle sum difference formula includes a sinusoidal formula for the sum of two angles.

The cosine formula for the sum of two angles.

The tangent of the sum of the two angles.

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

They are all deformed on the basis of this formula. Divide the first two formulas to get the tangent formula corresponding to repentance. When the length of two sides and the degree of their angle are known, or the degree of two angles and the length of one side, or the length of the three sides is known, the other angles and sides can be calculated using these rules.

What is the formula for the sum of the two angles and the difference of the trigonometric function.

cos(α+cosα·cosβ-sinα·sinβcos(α-cosα·cosβ+sinα·sinβsin(α+sinα·cosβ+cosα·sinβsin(α-sinα·cosβ-cosα·sinβtan(α+tanα+tanβ)/1-tanα·tanβ)tan(α-tanα-tanβ)/1+tanα·tanβ)cot(a+b) =cotacotb-1)/(cotb+cota)cot(a-b) =cotacotb+1)/(cotb-cota)

The derivation process of the sum angle formula failed:

In the rectangular coordinate system of the canopy cherry surface, the x-axis is used as the starting edge, the angle and the corner chain are used as the dry bush, and the unit vectors of the final edge are recorded as a and b respectively, and the coordinate method is used to represent the two vectors as a=(sin, cos), b=(sin, cos).

a·b=|a||b|cos, and a·b=sin ·sin +cos ·cos, and |a|=|b|=1。

cos=cos(α-cosα·cosβ+sinα·sinβ。

Replace with - to get cos( +cos ·cos -sin ·sin .

From the induction formula, sin( -cos[( 2]=-cos[( 2)- cos( +2)·cos +sin( +2)·sin ]=sin ·cos +cos ·sin ]=sin ·cos -cos ·sin.

In the same way, sin( +sin ·cos +cos +cos ·sin .

tan(α-sin(α-cos(α-sinα·cosβ-cosα·sinβ)/cosα·cosβ+sinα·sinβ)；In addition to cos ·cos, tan (-tan -tan ) 1 + tan · tan ).

In the same way, tan( +tan +tan ) 1-tan ·tan ).

1） sin（α+sinαcosβ+cosαsinβ；

2） cos（α+cosαcosβ-sinαsinβ；

The idea of the textbook is early in the Cartesian coordinate system.

, according to the formula for the distance between two points, deduced:

cos（α+cosαcosβ-sinαsinβ；

Then use the induction formula.

Proof: sin( +sin cos +cos sin ;

As shown in the figure: aod= ,bod=- aoc= ,doc= + then b(cos,-sin); d（1,0）；a（cosα,sinα）；c[cos（α+sin（α+

oa=ob=oc=od=1

cd=ab.

cd2=[cos（α+1] 2+[ sin（α+0] 2；

cos2（α+2cos（α+1 + sin2（α+2-2 cos（α+

ab2=（cosα-cosβ）2+ （sinα+sinβ）2；

cos2α-2cosαcosβ+cos2β+sin2α+2sinαsinβ+ sin2β；

2-2[cosαcosβ- sinαsinβ].

2-2 cos( + round mask = 2-2 [cos cos - sin sin].).

cos（α+cosαcosβ- sinαsinβsin（α+cos（90°-α

cos[（90°-α

cos（90°-αcos（-βsin（90°-αsin（-βsinαcosβ+cosαsinβ；

Proving that sin( + and cos( + is the basis for further proving most trigonometric formulations using the unit circle method.

1、sin（α+sinαcosβ+ cosαsinβ

In the Cartesian coordinate system, the Swift Collision takes the origin of the Luhong o as the center of the Changshu circle as the unit circle, and makes the following line segments in the unit circle:

The formula of the sum and difference of the two angles is the basis of the identity transformation of trigonometric functions, and other trigonometric formulas are deformed on the basis of this formula. For example, the formula of the double angle in the number of trigonometric roll masses is derived based on the formula of the sum of the two angles. What is the formula for the sum of the two angles and the difference of the trigonometric function.

The two-angle 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 sum of the two angles and the difference formula sine formula: sin( +sin ·cos +cos ·sin ; sin(α-sinα·cosβ-cosα·sinβ

The sum of the two angles and the difference formula sinusoidal formula: cos( +cos ·cos -sin ·sin ; cos(α-cosα·cosβ+sinα·sinβ

The sum of the two angles and the difference formula sinusoidal formula: tan ( +tan +tan ) 1-tan ·tan ); tan(α-tanα-tanβ)/1+tanα·tanβ)

Derivation of the formula for the sum of the two angles and the difference of the trigonometric function.

The two corners and the difference between the two corners'The formula is the basis of the identity transformation of trigonometric functions, and other trigonometric formulas are deformed on the basis of this formula. For example, the formula of double angles in trigonometric functions is derived based on the formula of the sum of two angles.

sin2α=2sinαcosα，cos2α=cos2α-sin2α=2cos2α-1=1-sin2α，tan2α=2tanα/（1-tan2α）

According to the formula of the sum of two angles, the angle under the common angle system can be expressed as: sin(90° + cos ; cos（90°+αsinα；tan（90°+αcotα；sin(90°－αcosα；cos(90°－αsinα；tan(90°－αcotα.

Trigonometric functions, two angles, and difference formulas memorize formulas.

Sine with different names, cosine with the same name plus or minus different, tangent is proportional to the remainder. The symbol of the sine formula is the same, and the cosine formula is positive and negative.