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.