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AP EAMCET · Maths · Trigonometric Ratios & Identities

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

  1. A \(\frac{1}{2 \sqrt{2}}\)
  2. B \(\frac{-1}{2 \sqrt{2}}\)
  3. C \(\frac{1}{\sqrt{3}}\)
  4. D \(\frac{-1}{\sqrt{3}}\)
Verified Solution

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}…