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$\sin (15^\circ) \cos (15^\circ)$ Multiply and divide by $2$. $\dfrac{2}{2} \sin (15^\circ) \cos (15^\circ)$ Use the double-angle identity: $\sin (2\theta) = 2 \sin (\theta) \cos (\theta)$ $\dfrac{1}{2} \sin(2 \cdot 15^\circ)$ Simplify. $\dfrac{1}{2} \sin (30^\circ)$ Use the unit circle: $\sin (30^\circ) = \frac{1}{2}$ $\dfrac{1}{2} \cdot \dfrac{1}{2}$ Simplify. $\boxed{\dfrac{1}{4}}$
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Mon, 12 Apr 2021 22:02 GMT