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:

Double angle formula

sin2α=2sinαcosα

tan2α=2tanα/( 1-tan^2(α))

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

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

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。