`{(sinα+sinβ=(\sqrt{2})/2),(cosα+cosβ=(\sqrt{6})/2):}`

`<=>{(sin²α+2sinαsinβ+sin²β=1/2(1)),(cos²α+2cosαcosβ+cos²β=3/2(2)):}`

Lấy `(1)+(2)`

`=>sin²α+2sinαsinβ+sin²β+cos²α+2cosαcosβ+cos²β=1/2+3/2`

`<=>2sinαsinβ+2cosαcosβ+2=2`

`<=>2sinαsinβ+2cosαcosβ=0`

`<=>2cos(α-β)=0`

`=>cos(α-β)=0`