Question

已知cosa=1/7,cos(a+β)=-11/14,且a,β∈(0,π/2)

Answer 1

cosa=1/7

sinα = 4√3/7,

cos(a+β)=-11/14

sin(α+β)= 5√3/14,

cos(α+β)=cosαcosβ - sinαsinβ

= 1/7*cosβ - 4√3/7*sinβ

= -11/14,

sin(α+β)=sinαcosβ + cosαsinβ

=4√3/7*cosβ +1/7*sinβ

=5√3/14

解上述关于 sinβ、cosβ 的二元一次方程组,得

sinβ =√3/2、

cosβ = 1/2.