sin2A=2sinA cosA

cos2a=cos^2 a-sin^2 a= 1-2sin^2 a=2cos^2 a- 1

tan2A=(2tanA)/( 1-tan^2 A)

Triple angle formula

sin3α=4sinα sin(π/3+α)sin(π/3-α)

cos3α=4cosα cos(π/3+α)cos(π/3-α)

tan3a = tan a tan(π/3+a) tan(π/3-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 difference product

sinθ+sinφ= 2 sin[(θ+φ)/2]cos[(θ-φ)/2]

sinθ-sinφ= 2 cos[(θ+φ)/2]sin[(θ-φ)/2]

cosθ+cosφ= 2 cos[(θ+φ)/2]cos[(θ-φ)/2]

cosθ-cosφ=-2 sin[(θ+φ)/2]sin[(θ-φ)/2]

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

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

Sum difference product

cos(α+β)=cosαcosβ-sinαsinβ

cos(α-β)=cosαcosβ+sinαsinβ

sin(α+β)=sinαcosβ+cosαsinβ

sin(α-β)=sinαcosβ -cosαsinβ

Sum and difference of products

sinαsinβ = [cos(α-β)-cos(α+β)] /2

cosαcosβ = [cos(α+β)+cos(α-β)]/2

sinαcosβ = [sin(α+β)+sin(α-β)]/2

cosαsinβ = [sin(α+β)-sin(α-β)]/2

Inductive formula

Sine (-α) =-Sine α

cos(-α) = cosα

tan (-α)=-tanα

sin(π/2-α) = cosα

cos(π/2-α) = sinα

sin(π/2+α) = cosα

cos(π/2+α) = -sinα

Sine (π-α) = Sine α

cos(π-α) = -cosα

Sine (π+α) =-Sine α

cos(π+α) = -cosα

tanA= sinA/cosA

tan(π/2+α)=-cotα

tan(π/2-α)=cotα

tan(π-α)=-tanα

tan(π+α)=tanα

Other formulas

( 1)(sinα)^2+(cosα)^2= 1

(2) 1+(tanα)^2=(secα)^2

(3) 1+(cotα)^2=(cscα)^2

(4) For any non-right triangle, there is always tana+tanbtana+tanb+tanc = tanatanbtanc.

(5)cotAcotB+cotAcotC+cotbctc = 1

(6) Cost (A/2)+ Cost (B/2)+ Cost (C/2)= Cost (A/2) Cost (B/2)

(7)(cosa)^2+(cosb)^2+(cosc)^2= 1-2cosacosbcosc

(8)(sina)^2+(sinb)^2+(sinc)^2=2+2cosacosbcosc