If sin (2a + 45°) = cos (30° – a), where 0°

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If sin (2a + 45°) = cos (30° – a), where 0° < a < 90°, then the value of a is :

1. 0°
2. 15°
3. 45°
4. 60°

Correct Option: B

sin (2a + 45°) = cos (30° – a)
⇒ sin (2a + 45°) = sin {90° – (30° – a) }
⇒ sin (2a + 45°) = sin (60° + a)
[∵ sin (90° – θ) = cosθ]
⇒ 2a + 45° = 60° + a
⇒ 2a – a = 60° - 45°
⇒ a = 15°