Sine formula of the sum of two angles: sin (α+β) = sin α cos β+cos α sin β.

Sine formula of the difference between two angles: sin (α-β) = sin α cos β-cos α sin β.

Cosine formula of the sum of two angles: cos (α+β) = cos α cos β-sin α sin β.

Cosine formula of the difference between two angles: cos (α-β) = cos α cos β+sin α sin β.

Tangent formula of the sum of two angles: tan (α+β) = (tan α+tan β)/(1-tan α tan β)

Tangent formula of the difference between two angles: tan (α-β) = (tan α-tan β)/(1+tan α-tan β)

Double angle sine, cosine and tangent formulas;

sin2α=2sinαcosα

cos2α=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)

tan2α=2tanα/[ 1-tan^2(α)]

Sine, cosine and tangent formulas of half angle;

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)=( 1-cosα)/sinα= sinα/( 1+cosα)