JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(\sin\left(\dfrac{\pi}{18}\right) \sin\left(\dfrac{5\pi}{18}\right) \sin\left(\dfrac{7\pi}{18}\right) = K\), then the value of \(\sin\left(\dfrac{10K\pi}{3}\right)\) is :
- A \(\dfrac{\sqrt{3} + 1}{2\sqrt{2}}\)
- B \(\dfrac{\sqrt{3} - 1}{\sqrt{2}}\)
- C \(\dfrac{\sqrt{3}}{2}\)
- D \(\dfrac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{\sqrt{3} + 1}{2\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Given \(K = \sin\left(\dfrac{\pi}{18}\right) \sin\left(\dfrac{5\pi}{18}\right) \sin\left(\dfrac{7\pi}{18}\right)\) Using the standard trigonometric identity…
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