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Find sin 15° .
1. \(\frac{\sqrt3-1}{2\sqrt2}\)
2. \(​​​​\frac{\sqrt3-2}{\sqrt2}\)
3. \(\frac{\sqrt3}{2\sqrt2}\)
4. \(\frac{3-\sqrt2}{\sqrt2}\)

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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° = \(\frac{\sqrt3-1}{2\sqrt2}\)

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