Sin- 14 sin 3 - 14 sin 5 - 14 sin 7 - 14 sin 9 - 14 sin 11 - 14 sin 13 - 14 is equal to

sin(π14)sin(3π14)sin(5π14)sin(7π14)sin(9π14)sin(11π14)sin(13π14) sinθ=sin(π θ) sin(9π14)=sin(π 9π14)=sin(5π14) sin(11π14)=sin(3π14) #160; ...

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Product of Trigonometric Ratios in Terms of Their Sum

sinπ/ 14 sin ...

Question

$sin \frac{π}{14} sin \frac{3 π}{14} sin \frac{5 π}{14} sin \frac{7 π}{14} sin \frac{9 π}{14} sin \frac{11 π}{14} sin \frac{13 π}{14}$ is equal to

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sin \frac{π}{14} sin \frac{3 π}{14} sin \frac{5 π}{14} sin \frac{7 π}{14} sin \frac{9 π}{14} sin \frac{11 π}{14} sin \frac{13 π}{14}

sin \frac{π}{14} sin \frac{3 π}{14} sin \frac{5 π}{14} sin \frac{7 π}{14} sin \frac{9 π}{14} sin \frac{11 π}{14} sin \frac{13 π}{14} = \frac{1}{k},

k

sin \frac{π}{14} sin \frac{3 π}{14} sin \frac{5 π}{14} sin \frac{7 π}{14} sin \frac{9 π}{14} sin \frac{11 π}{14} sin \frac{13 π}{14}

k^{2}

k^{2}

sin \frac{π}{14} sin \frac{3 π}{14} sin \frac{5 π}{14} sin \frac{7 π}{14} sin \frac{9 π}{14} sin \frac{11 π}{14} sin \frac{13 π}{14} = \frac{1}{k},

k

s i n \frac{π}{14} s i n \frac{3 π}{14} s i n \frac{5 π}{14} s i n \frac{7 π}{14} s i n \frac{9 π}{14} s i n \frac{11 π}{14} s i n \frac{13 π}{14}

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