The value of sin- 14 sin3- 14 sin5- 14 sin7- 14 sin9- 14 sin11- 14 sin13- 14 is equal to

Sinπ 14 sin3π 14 sin5π 14 sin7π 14 sin9π 14 sin11π 14 sin13π 14 =sinπ 14 sin3π 14 sin5π 14× 1×sin(π 5π 14) sin(π 3π 14) sin(π π 14) =[sinπ 14 sin3π 14 sin5π 1 ...

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Byju's Answer

Standard XII

Mathematics

Product of Trigonometric Ratios in Terms of Their Sum

The value of ...

Question

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

$\frac{1}{8}$

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$\frac{1}{16}$

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$\frac{1}{32}$

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$\frac{1}{64}$

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Solution

The correct option is D
$\frac{1}{64}$

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

$= sin \frac{π}{14} sin \frac{3 π}{14} sin \frac{5 π}{14} \times 1 \times sin (π - \frac{5 π}{14}) sin (π - \frac{3 π}{14}) sin (π - \frac{π}{14})$

= $[sin \frac{π}{14} sin \frac{3 π}{14} sin \frac{5 π}{14} sin \frac{7 π}{14}]^{2} = \frac{1}{64}$

Suggest Corrections

The value of sinπ14 sin3π14 sin5π14 sin7π14 sin9π14 sin11π14 sin13π14 is equal to

The correct option is D 164 sinπ14 sin3π14 sin5π14 sin7π14 sin9π14 sin11π14 sin13π14 =sinπ14 sin3π14 sin5π14×1×sin(π−5π14) sin(π−3π14) sin(π−π14) =[sinπ14 sin3π14 sin5π14 sin7π14]2=164

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