Search any question & find its solution
Question:
Answered & Verified by Expert
The value of \(\left(\sin 210^{\circ}\right)\left(\sin 585^{\circ}\right)\) is
Options:
Solution:
1309 Upvotes
Verified Answer
The correct answer is:
\(\frac{1}{2 \sqrt{2}}\)
\(\begin{aligned}
\sin 210^{\circ} \cdot \sin 585^{\circ} & =\sin \left(180^{\circ}+30^{\circ}\right) \cdot \sin \left(540^{\circ}+45^{\circ}\right) \\
& =-\sin 30^{\circ}\left(-\sin 45^{\circ}\right) \\
& =\frac{-1}{2} \times \frac{-1}{\sqrt{2}}=\frac{1}{2 \sqrt{2}}
\end{aligned}\)
Hence, option (a) is correct.
\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.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.