The value of sin $105^{0}$ is

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

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

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

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

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Solution

The correct option is C $\frac{\sqrt{3} + 1}{2 \sqrt{2}}$
The value of $sin 105^{\circ} = sin (60^{\circ} + 45^{\circ})$
$= sin 60^{\circ} . cos 45^{\circ} + sin 45^{\circ} . cos 60^{\circ}$
$= \frac{\sqrt{3}}{2} . \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} . \frac{1}{2}$
$= \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

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