Найти tgβ если cos(α+β)/cos(α-β)=2/3; ctgα=5

Question

Найти tgβ если cos(α+β)/cos(α-β)=2/3; ctgα=5

Answer 1

Cos(α+β)/cos(α-β)=2/3
3cos(α+β) = 2cos(α-β)
3(cosα*cosβ - sinα*sinβ) = 2(cosα*cosβ + sinα*sinβ)

cosα*cosβ = 5sinα*sinβ
ctgα*ctgβ = 5
ctgβ = 1
tgβ = 1/ctgβ = 1