If sin(α + β) = 1 And sin(α – β) = 1/2, where , then find the values of tan(α + 2β) And tan(2α + β).

Question

Philoid · Accepted Answer

Given sin(α + β) = 1 And sin(α – β) = 1/2

⇒ α + β = 90° …(1) And α - β = 30° …(2)

Adding(1) And(2),

⇒ 2α = 120°

∴ α = 60°

Subtracting(2) from(1),

⇒ 2β = 60°

∴ β = 30°

Then,

∴ tan(α + 2β) = tan(60° + 2 × 30°) = tan 120° = -√3

And tan(2α + β) = tan(2 × 60° + 30°) = tan 150° = -(1/√3)