Question

The value of $\left(\sin 210^{\circ}\right)\left(\sin 585^{\circ}\right)$ is

• A. $\frac{1}{2 \sqrt{2}}$
• B. $\frac{-1}{2 \sqrt{2}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{-1}{\sqrt{3}}$

Answer 1

Answer: (A)

$\sin 210^{\circ} \cdot \sin 585^{\circ}=\sin \left(180^{\circ}+30^{\circ}\right) \cdot \sin \left(540^{\circ}+45^{\circ}\right)$
$=-\sin 30^{\circ}\left(-\sin 45^{\circ}\right)$
$=\frac{-1}{2} \times \frac{-1}{\sqrt{2}}=\frac{1}{2 \sqrt{2}}$