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

Question

Aicharya · Accepted Answer

$\begin{aligned} \sin 210^{\circ} \cdot \sin 585^{\circ} & =\sin \left(180^{\circ}+30^{\circ}\right) \cdot \sin \left(540^{\circ}+45^{\circ}\right) \ & =-\sin 30^{\circ}\left(-\sin 45^{\circ}\right) \ & =\frac{-1}{2} \times \frac{-1}{\sqrt{2}}=\frac{1}{2 \sqrt{2}} \end{aligned}$ Hence, option (a) is correct.

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

Solution