If cos (π)/7 cos (2 π)/7 cos (4 π)/7=(sin (8 π)/7)/(8 sin (π)/7) then, sin (π)/14 sin (3 π)/14 sin (5 π)/14 sin (7 π)/14 sin (9 π)/14 sin (11 π)/14…

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If cos (π)/7 cos (2 π)/7 cos (4 π)/7=(sin (8 π)/7)/(8 sin (π)/7) then, 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=

MARKS Content Team · Accepted Answer

Correct answer: (C) 1/64. 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 ∵ sin (13 π)/14=sin (π-(π)/14 )=sin (π)/14 sin (11 π)/14=sin (π-(3 π)/14 )=sin (3 π)/14 sin (9 π)/14=sin (π-(5 π)/14 )=sin (5 π)/14 = (sin^2 (π)/14 · sin^2 (3 π)/14 · sin^2 (5 π)/14 ) =cos^2 ((π)/2-(5 π)/14 ) · cos^2 ((π)/2-(3 π)/14 ) · cos^2 ((π)/2-(π)/14 ) =cos^2 (π)/7 · cos^2 (2 π)/7 · cos^2 (4 π)/7 = ((sin (8 π)/7)/(8 sin (π)/7) )^2= ((-sin (π)/7)/(8 sin (π)/7) )^2=1/64 .

If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$ then, $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14}=$

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