Correct Answer - Option 1 :

\(\frac{\sqrt3-1}{2\sqrt2}\)
**Concept:**

sin (A – B) = sinA cosB – cosA sinB

**Calculation:**

sin 15° = sin (45 – 30)

⇒ sin (45 – 30) = sin 45 cos 30 – cos45 sin30

⇒ sin (45 – 30) = (1/√2) × (√3/2) – (1/√2) × (1/2)

⇒ sin (45 – 30) = \(\frac{\sqrt3}{2\sqrt2}-\frac{1}{2\sqrt2}\)

**⇒ sin 15° = \(\frac{\sqrt3-1}{2\sqrt2}\)**