Question

已知α,β为锐角,cosα=4／5,tan(α-β)= -1/3,求cosβ的值

Answer 1

∵cosα=4/5 ∴sinα=3/5

sin(α-β)=sinαcosβ-cosαsinβ

cos(α-β)=cosαcosβ+sinαsinβ

tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)

=(3/4-tanβ)/(1+3tanβ/4)=-1/3

3/4-tanβ=-1/3-tanβ/4

3/4+1/3 =3tanβ/4. tanβ=13/9

cosβ=9/√13²+9²=9/√250=9/5√10