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