S use sin Rule and cosine Rule, Identitiogs following without 9 to evaluate the for calculator D $$ \sin 15^{\prime} \cos 15^{\circ} $$

Question

UpStudy AI · Accepted Answer

We start with the product
$$
\sin 15^\circ \cos 15^\circ.
$$

A useful identity for the product of $$\sin$$ and $$\cos$$ of the same angle is
$$
\sin \theta \cos \theta = \frac{1}{2} \sin (2\theta).
$$

Taking $$\theta = 15^\circ$$, we get
$$
\sin 15^\circ \cos 15^\circ = \frac{1}{2} \sin (2 \times 15^\circ) = \frac{1}{2} \sin 30^\circ.
$$

We know that
$$
\sin 30^\circ = \frac{1}{2}.
$$

Thus,
$$
\frac{1}{2} \sin 30^\circ = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.
$$
$$ \sin 15^\circ \cos 15^\circ = \frac{1}{4} $$

S use sin Rule and cosine Rule, Identitiogs following without 9 to evaluate the for calculator D \( \sin 15^{\prime} \cos 15^{\circ} \)