Question

设cosα=1/3，cosβ=2/3，αβ∈(0，π/2)，求cos(α+β)

Answer 1

和差公式，由题意得sinα=2√2/3，sinβ=√5/3，
代入cos(α十β)=cosαcosβ－sinαsinβ
得2/9－2√10/9

Answer 2

α,β∈(0，π/2)
cosα=1/3 =>sinα=2√2/3
cosβ=2/3 =>cosβ=√5/3
cos(α+β)
=cosα.cosβ-sinα.sinβ
=(1/3)(2/3)-(2√2/3)(√5/3)
=2/9 - 2√10/9