1 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)]
2. 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]cos[(α-β)/2]; cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]
3 triple angle formula. sin3α=3sinα-4sin^3α:cos3α=4cos^3α-3cosα
The trigonometric function relationship between the sum and difference of two angles, sin (α+β) = sin α cos β+cos α sin β; sin(α-β)= sinαcosβ-cosαsinβ; cos(α+β)= cosαcosβ-sinαsinβ; cos(α-β)= cosαcosβ+sinαsinβ; tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ); tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)