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)

cot(a+b)=(cota cotb- 1)/(cot b+cota)？

cot(a-b)=(cota cotb+ 1)/(cot b-cota)

Double angle formula

tan2a=2tana/[ 1-(tana)^2]

cos2a=(cosa)^2-(sina)^2=2(cosa)^2 - 1= 1-2(sina)^2

sin2a=2sina*cosa

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))

cot(a/2)=√(( 1+cosa)/(( 1-cosa))cot(a/2)=-√(( 1+cosa)/(( 1-cosa))？

Tan(a/2)=( 1-cosa)/ Sina = Sina /( 1+cosa)

Sum difference product

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

Product sum and difference formula

sin(a)sin(b)=- 1/2 *[cos(a+b)-cos(a-b)]

cos(a)cos(b)= 1/2 *[cos(a+b)+cos(a-b)]

sin(a)cos(b)= 1/2 *[sin(a+b)+sin(a-b)]

Inductive formula

sin(-a)=-sin(a)

cos(-a)=cos(a)

sin(π/2-a)= cos(a)

cos(π/2-a)= sin(a)

sin(π/2+a)= cos(a)

cos(π/2+a)=-sin(a)

sin(π-a)= sin(a)

cos(π-a)=-cos(a)

sin(pi+a)=-sin(a)

cos(pi+a)=-cos(a)

tga=tana=sina/cosa

General formula of trigonometric function

sin(a)=(2tan(a/2))/( 1+tan^2(a/2))

cos(a)=( 1-tan^2(a/2))/( 1+tan^2(a/2))

Tan (1) = (1)

Other formulas

A * sin (a)+b * cos (a) = sqrt (a2+B2) sin (a+c) [where tan(c)=b/a]

A * sin (a)-b * cos (a) = sqrt (a2+B2) cos (a-c) [where tan(c)=a/b]

1+sin(a)=(sin(a/2)+cos(a/2))^2

1-sin(a)=(sin(a/2)-cos(a/2))^2

Other non-critical trigonometric functions

csc(a)= 1/sin(a)

Seconds (a)= 1/ cosine (a)

Hyperbolic function

sinh(a)=(e^a-e^(-a))/2

cosh(a)=(e^a+e^(-a))/2

Tgh(a)=sinh(a)/cosh(a)) I hope to adopt it.