1、sin(A+B) = sinAcosB+cosAsinB .

sin(A-B) = sinAcosB-cosAsinB .

3、cos(A+B) = cosAcosB-sinAsinB .

4、cos(A-B) = cosAcosB+sinAsinB .

5、tan(A+B)=(tanA+tanB)/( 1-tanA tanB)。

6、tan(A-B)=(tanA-tanB)/( 1+tanA tanB)。

7、cot(A+B)=(cotA cotB- 1)/(cot B+cotA)。

8、cot(A-B)=(cotA cotB+ 1)/(cot b-cotA)。

1, sum of two angles formula

sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa

cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb

tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)

ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)

2. Double angle formula

tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA

cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

3. Half-angle formula

sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)

cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)

tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))

ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))

Brief introduction of trigonometric function:

Trigonometric function is a transcendental function in elementary functions in mathematics. Their essence is the mapping between any set of angles and a set of ratio variables. The usual trigonometric function is defined in a plane rectangular coordinate system.

Its definition field is the whole real number field. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.