In sin (α + β) = 1, sin(α – β) = 1/2, then tan (α + 2β) tan (2α +

| In sin (α + β) = 1, sin(α – β) = 1/2, then tan (α + 2β) tan (2α + β) = ?

A. -1

B. 0

C. None of these

D. 1

Please scroll down to see the correct answer and solution guide.

⇒ sin(α – β) = 1/2

⇒ sin(α – β) = sin30°

⇒ (α – β) = 30° ...(1)

⇒ sin (α + β) = 1

⇒ sin (α + β) = sin90°

⇒ (α + β) = 90° ...(2)

From equation (1) and equation (2)

⇒ α = 60° and β = 30°

⇒ tan (α + 2β) tan (2α + β)

⇒ tan(60° + 2 × 30°) tan (2 × 60° + 30°)

⇒ tan120° tan150°

⇒ tan(90° + 30°) tan(90° + 60°)

⇒ -cot30° (-cot60°)

⇒ 1