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Existence of Limit

The value of ...

Question

The value of $sin 15^{\circ}$ is

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is D $\frac{\sqrt{3} - 1}{2 \sqrt{2}}$
$s i n 15^{\circ} = s i n (60 - 45) = s i n 60 c o s 45 - c o s 60 s i n 45$
$\Rightarrow \frac{\sqrt{3}}{2} \frac{1}{\sqrt{2}} - \frac{1}{2} . \frac{1}{\sqrt{2}} = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$

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Similar questions

\begin{matrix} cos 15^{\circ} = \frac{\sqrt{3} + 1}{2 \sqrt{2}} sin 15^{\circ} = \frac{\sqrt{3} - 1}{2 \sqrt{2}} \end{matrix}

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