cos(α-β) = cosαcosβ + sinαsinβ
Therefore, the expression sinαsinβ + cosαcosβ - cos(α-β) simplifies to:
sinαsinβ + cosαcosβ - (cosαcosβ + sinαsinβ)
Simplifying further:
sinαsinβ + cosαcosβ - cosαcosβ - sinαsin= cosαcosβ - cosαcos= 0
Therefore, the final answer is 0.
cos(α-β) = cosαcosβ + sinαsinβ
Therefore, the expression sinαsinβ + cosαcosβ - cos(α-β) simplifies to:
sinαsinβ + cosαcosβ - (cosαcosβ + sinαsinβ)
Simplifying further:
sinαsinβ + cosαcosβ - cosαcosβ - sinαsin
= cosαcosβ - cosαcos
= 0
Therefore, the final answer is 0.