Value of sin 15⁰

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$\frac{\sqrt{3} + 1}{\sqrt{2}}$

$\frac{\sqrt{3} + 1}{2 \sqrt{2}}$

$\frac{\sqrt{3} - 1}{2 \sqrt{2}}$

$\frac{\sqrt{3} - 1}{\sqrt{2}}$

answer is A.

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Detailed Solution

$\sin 15^{0} = \sin (45^{0} - 30^{0}) = \sin 45^{0} \cos 30^{0} - \cos 45^{0} \sin 30^{0} = \frac{\sqrt{3}}{2 \sqrt{2}} - \frac{1}{2 \sqrt{2}} = \frac{\sqrt{3} - 1}{2 \sqrt{2}} ∴ \sin 15^{0} = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$

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