What is the trigonometric formula? Trigonometric formula is a trigonometric function, which belongs to transcendental function in elementary function in mathematics. 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.
Formulas of trigonometric functions's sum formula of two corners in junior high school mathematics
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
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)
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))
Sum-difference product formula
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)
2cosAcosB=cos(A+B)-sin(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2
cosA+cosB = 2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
tanA-tanB=sin(A-B)/cosAcosB
Double angle formula
Sin2A=2SinA。 Kosa
cos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1
tan2A=(2tanA)/( 1-tanA^2)
(Note: Sina 2 is the square of Sina 2 (a))
half-angle formula
tan(A/2)=( 1-cosA)/sinA = sinA/( 1+cosA)；
cot(A/2)= sinA/( 1-cosA)=( 1+cosA)/sinA。
sin^2(a/2)=( 1-cos(a))/2
cos^2(a/2)=( 1+cos(a))/2
tan(a/2)=( 1-cos(a))/sin(a)= sin(a)/( 1+cos(a))
Sum and difference formula of product
sinαsinβ=[cos(α-β)-cos(α+β)]/2
cosαcosβ=[cos(α+β)+cos(α-β)]/2
sinαcosβ=[sin(α+β)+sin(α-β)]/2
sinα=2tan(α/2)/[ 1+tan^(α/2)]
cosα=[ 1-tan^(α/2)]/ 1+tan^(α/2)]
tanα=2tan(α/2)/[ 1-tan^(α/2)]