The value of $sin 75^{0} =$

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

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

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

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Solution

The correct option is C $\frac{\sqrt{3} + 1}{2 \sqrt{2}}$
$cos 30^{\circ} = \frac{\sqrt{3}}{2}$
$\Rightarrow 2 {cos}^{2} 15^{\circ} - 1 = \frac{\sqrt{3}}{2}$
$\Rightarrow {cos}^{2} 15^{\circ} = \frac{\sqrt{3} + 2}{4}$
$\Rightarrow {cos}^{2} 15^{\circ} \frac{4 + \sqrt{3}}{8}$
$∴ cos 15^{\circ} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$
$sin 75^{\circ} = cos 15^{\circ} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

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