已知cos(θ+π/6)=5/13,θ∈(0,π/2),求cosθ

题目

已知cos(θ+π/6)=5/13,θ∈(0,π/2),求cosθ

答案

cos(θ+π/6)=5/13 θ∈(0,π/2),
sin(θ+π/6)=12/13
cosθ
=cos(θ+π/6-π/6)
=cos(θ+π/6)cos(π/6)+sin(θ+π/6)sin(π/6)
=5/13*√3/2+12/13x1/2
=(5√3+12)/26