cos(α+β)= cosαcosβ-sinαsinβcos(α-β)= cosαcosβ+sinαsinβsin(αβ)= sinαcosβcosαsinβtan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)=(tanα-tanβ)/( 1+tanαtanβ)

Sum-difference product formula

sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]sinα-sinβ= 2 cos[(α+β)/2]sin[(α-β)/2]cosα+cosβ= 2 cos[(α+β)/2]cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]

Product sum and difference formula

sinαcosβ=( 1/2)[sin(α+β)+sin(α-β)]cosαsinβ=( 1/2)[sin(α+β)-sin(α-β)]cosαcosβ=( 1/2)[cos(α+β)+cos(α-β)]sinαsinβ=-( 1/2)[cos(α+β)-cos(α-β)]

Double angle formula

sin(2α)= 2 sinαcosα= 2/(tanα+cotα)cos(2α)=(cosα)^2-(sinα)^2=2(cosα)^2- 1= 1-2(sinα)^2tan(2α)=2tanα/( 1-tan^2α)cot(2α)=(cot^2α- / kloc-0/)/(2cotα)sec(2α)=sec^2α/( 1-tan^2α)CSC(2α)= 1/2 * secαCSCα

Triple angle formula

sin(3α)=3sinα-4sin^3α= 4 sinαsin(60+α)sin(60-α)cos(3α)=4cos^3α-3cosα= 4 cosαcos(60+α)cos(60-α)tan(3α)=(3tanα-tan^3α)/( 1-3tan^2α)= tanαtan(π/ 3+α)tan(π/3-α)cot(3α)=(cot^3α-3cotα)/(3cot^2α- 1)

N times angle formula

sin(nα)=ncos^(n- 1)αsinα-c(n,3)cos^(n-3)αsin^3α+c(n,5)cos^(n-5)αsin^5α-…cos(nα)=cos^nα-c(n,2)cos^(n-2)αsin^2α+c(n,4)cos^(n-4)αsin^4α-…

half-angle formula

sin(α/2)=√(( 1-cosα)/2)cos(α/2)=√(( 1-cosα)/2)tan(α/2)=√(( 1-cosα)/( 1+cosα))= sinα/( 1+cosα)=( 1-cosα)/sinαcot(α/2)=√(( 1

Auxiliary angle formula

asinα+bcosα=√(a^2+b^2)sin(α+arctan(b/a))asinα+bcosα=√(a^2+b^2)cos(α-arctan(a/b))

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

Reduced power formula

sin^2α=( 1-cos(2α))/2=versin(2α)/2 cos^2α=( 1+cos(2α))/2=covers(2α)/2tan^2α=( 1-cos(2α))/( 1+cos(2α))

Trigonometric function of trigonometric sum

sin(α+β+γ)= sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ-sinαsinβsinγcos(α+β+γ)= cosαcosβcosγ-cosαsinγ-sinαcosβsinγ-sinαsinβcosγtan(α+β+γ) =(tanα+tanβ+tanγ-tanαtanβtanβtanγ)/( 1-tanαtanβtanγtanγ-tanγtanγtanα

Other formulas

1+sin(a)=(sin(a/2)+cos(a/2))^2 1-sin(a)=(sin(a/2)-cos(a/2))^2 CSC(a)= 1/sin(a)sec(a)= 1/cos(a)cos 30 = sin 60 sin 30 = cos 60

Derived formula

tanα+cotα= 2/sin2αtanα-cotα=-2 cot 2α 1+cos2α=2cos^2α 1-cos2α=2sin^2α 1+sinα=[sin(α/2)+cos(α/2)]^2