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  4. Continued product cos α cos 2 α cos 22 α cos 2 n -1 α <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/mathematics/43ada9be9046d498cfa119d24f8ba533-.png /> Where, n ∈ I (Integer) The value of sin ((π/14)) sin ((3 π/14)) sin ((5 π/14)) sin ((7 π/14)) sin ((9 π/14)) sin ((11 π/14)) sin ((13 π/14)) is -

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Q. Continued product $\cos \alpha \cos 2 \alpha \cos 2^2 \alpha$ $\cos 2^{ n -1} \alpha$
image
Where, $n \in I$ (Integer)
The value of $\sin \left(\frac{\pi}{14}\right) \sin \left(\frac{3 \pi}{14}\right) \sin \left(\frac{5 \pi}{14}\right) \sin \left(\frac{7 \pi}{14}\right) \sin \left(\frac{9 \pi}{14}\right) \sin \left(\frac{11 \pi}{14}\right) \sin \left(\frac{13 \pi}{14}\right)$ is -

Trigonometric Functions

Solution:

Correct answer is (d) $\frac{1}{64}$