The sum of the two is still cosα+cosβ=2cos[(α+β)/2]·cos[(α-β)/2]

The sum of the two is sinα+sinβ=2sin[(α+β)/2]·cos[(α-β)/2]

The difference between the two is cosα-cosβ=-2sin[(α+β)/2]·sin[(α-β)/2]

The difference between the two is sinα-sinβ=2cos[(α+β)/2]·sin[(α-β)/2]