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)

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