∫cos(α+β)= cosαcosβ-sinαsinβ

Of course, there are cosα+cosβ=cosαcosβ-sinαsinβ.

It was established at that time. For example, when α = 90 and β = 0, the above formula holds.

Inductive formula used:

Inductive formula

Sine (-α) =-Sine α

cos(-α)=cosα

tan(-α)=-tanα

Kurt (-α) =-Kurt α

sin(π/2-α)=cosα

cos(π/2-α)=sinα

tan(π/2-α)=cotα

cot(π/2-α)=tanα

sin(π/2+α)=cosα

cos(π/2+α)=-sinα

tan(π/2+α)=-cotα

cot(π/2+α)=-tanα

Sine (π-α) = Sine α

cos(π-α)=-cosα

tan(π-α)=-tanα

cot(π-α)=-coα

Sine (π+α) =-Sine α

cos(π+α)=-cosα

tan(π+α)=tanα

cot(π+α)=cotα

sin(3π/2-α)=-cosα

cos(3π/2-α)=-sinα

tan(3π/2-α)=cotα

cot(3π/2-α)=tanα

sin(3π/2+α)=-cosα

cos(3π/2+α)=sinα

tan(3π/2+α)=-cotα

cot(3π/2+α)=-tanα

Sine (2π-α)=- Sine α

cos(2π-α)=cosα

tan(2π-α)=-tanα

Kurt (2π-α)=- Kurt α

sin(2kπ+α)=sinα

cos(2kπ+α)=cosα

tan(2kπ+α)=tanα

cot(2kπ+α)=cotα

(where k∈Z)

Sum angle formula:

Two-angle sum formula

cos(α+β)= cosαcosβ-sinαsinβcos(α-β)= cosαcosβ+sinαsinβ

sin(α+β)= sinαcosβ+cosαsinβsin(α-β)= sinαcosβ-cosαsinβ

The above formula can be directly used for calculation:

2.

( 1)cos75 =cos(30 +45)

(2)cos(- 165)= cos( 165)= cos(90+75)=-sin(75)=-sin(30+45)

(3)cos 7π/ 12 = cos(π/2+)=-sin(π/ 12)= sin 30

(4)cos(-6 1π/ 12)= cos(6 1π/ 12)= cos(5π+π/ 12)= cos(π+π/ 12)=-cos(π/ 12)