Find the exact value of $\sin 15^\circ$.

Question

Accepted Answer

$\dfrac{\sqrt{6} - \sqrt{2}}{4}$. Write $15^\circ = 45^\circ - 30^\circ$ and use $\sin(A - B) = \sin A\cos B - \cos A\sin B$: $\dfrac{\sqrt{2}}{2}\cdot\dfrac{\sqrt{3}}{2} - \dfrac{\sqrt{2}}{2}\cdot\dfrac{1}{2} = \dfrac{\sqrt{6} - \sqrt{2}}{4}$. The version with a plus sign is $\sin 75^\circ$.

Answer

A) $\dfrac{\sqrt{6} + \sqrt{2}}{4}$

Answer

B) $\dfrac{\sqrt{6} - \sqrt{2}}{4}$

Answer

C) $\dfrac{1}{4}$

Answer

D) $\dfrac{\sqrt{3} - 1}{2}$

Find the exact value of $\sin 15^\circ$.

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