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。