Let α and β be first quadrant angles with cos(α)=√5/5 and sin(β)=√3/6. Find cos(α−β).

Question

Let  and  be first quadrant angles with  and . Find cos(α−β).

Answer 1

cosα = √5/5 So, sinα = √(1 - cos²α) = 2√5/5

sinβ = √3/6 So, cosβ = √(1 - sin²β) = √33/6

cos(α - β) = cosαcosβ + sinαsinβ

Plug in the appropriate values and simplify,

Answer 2

Use the difference of angles formula.