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If α and β are positive acute angles, sin (4α – β) = 1 and cos (2 α + β) = (1 / 2) , then the value of sin (α + 2β) is
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- 0
- 1
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√3 2 -
1 √2
Correct Option: D
sin (4α – β) = 1 = sin 90°
⇒ 4α – β = 90° ...(i)
| cos (2α + β) = | = cos 60° | 2 |
⇒ 2α + β = 60° ...(ii)
On adding equations (i) and (ii),
4α - β + 2α + β = 90° + 60°
| ⇒ 6α = 150° ⇒ α = | = 25° | 6 |
From equation (ii),
2 × 25 + β = 60°
⇒ β = 60° – 50° = 10°
∴ sin (α + 2β)
= sin (25 + 2 × 10)
| = sin 45° = | = 25° | √2 |
