if sinα+sinβ=a and cosα+cosβ=b, then the value of coz(α+β) is

Dear Student

sinα+sinβ=a
on squaring
sin²α+sin²β+ 2 sinαsinβ=a²......(i)

cosα+cosβ=b
on squaring
cos²α+cos²β + 2.cosαcosβ=b².....(ii)
Adding equation i and ii
sin²α+sin²β+ 2sinαsinβ+cos²α+cos²β + 2.cosαcosβ = a² + b²
since sin²A + cos²A = 1
2 + 2(cosαcosβ+sinαsinβ) =a²+ b²
cos(α- β)=cosαcosβ+sinαsinβ= (a²+ b²–2)/2


Thanks