AP EAMCET · Maths · Trigonometric Ratios & Identities
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 & Solution
Correct Answer
(A) \(\frac{1}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\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}…
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