What is the value of $\sin 75^{\circ}$ ?

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

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

answer is C.

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Detailed Solution

$\sin 75^{\circ} = \sin (45 ° + 30 °) = \sin 45 ° \cos 30 ° + \cos 45 ° \sin 30 ° = \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}} \times \frac{1}{2} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

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