cos(α+β)=cosα cosβ-sinα sinβ

cos(α-β)=cosα cosβ+sinα sinβ

sin(α+β)=sinα cosβ+cosα sinβ

sin(α-β)=sinα cosβ-cosα sinβ

tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)

tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)

Double angle formula:

sin(2α)=2sinα cosα

cos(2α)=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)

tan(2α)=2tanα/[ 1-tan^2(α)]

Triple angle formula:

sin3α=3sinα-4sin^3(α)

cos3α=4cos^3(α)-3cosα

Half-angle formula:

sin^2(α/2)=( 1-cosα)/2

cos^2(α/2)=( 1+cosα)/2

tan^2(α/2)=( 1-cosα)/( 1+cosα)

tan(α/2)= sinα/( 1+cosα)=( 1-cosα)/sinα

General formula:

Sine, cosine and tangent formulas of half angle (power decreasing and angle expanding formulas)

sinα=2tan(α/2)/[ 1+tan^2(α/2)]

cosα=[ 1-tan^2(α/2)]/[ 1+tan^2(α/2)]

tanα=2tan(α/2)/[ 1-tan^2(α/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)]

Sum-difference product formula:

sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]

sinα-sinβ= 2cos[(α+β)/2]sin[(α-β)/2]

cosα+cosβ= 2cos[(α+β)/2]cos[(α-β)/2]

cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]