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° = \(\frac{\sqrt3-1}{2\sqrt2}\)