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]

Extended data:

Sum angle formula:

cos(α+β)=cosα cosβ-sinα sinβ？

cos(α-β)=cosα cosβ+sinα sinβ？

sin(α β)=sinα cosβ cosα sinβ？

tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)？

tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)

Basic relations of trigonometric functions with the same angle

Reciprocal relations: tanα cotα= 1+0, sin α CSC α = 1, cos α secα =1; +0;

The relationship of quotient: sinα/cosα=tanα=secα/cscα, cos α/sin α = cot α = CSC α/sec α;

And the relationship: sin2α+cos2α= 1, 1+tan2α=sec2α,1+cot2α = csc2α;

Square relation: sin? α+cos？ α= 1。