If k = sinπ18.sin5π18.sin7π18, then the numerical value of k i

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Question

If k = sin

\frac{π}{18}

.sin

\frac{5 π}{18}

.sin

\frac{7 π}{18}

, then the numerical value of k is

Options:

A . 14

B . 18

C . 116

D . None of these

Answer: Option B
:
B
(b) We havek = sin

\frac{π}{18}

.sin

\frac{5 π}{18}

.sin

\frac{7 π}{18}

= cos

(\frac{π}{2} - \frac{π}{18})

cos

(\frac{π}{2} - \frac{5 π}{18})

cos

(\frac{π}{2} - \frac{7 π}{18})

= cos

\frac{π}{9}

cos

\frac{2 π}{9}

cos

\frac{4 π}{9}

=

\frac{s i n 2^{3} \frac{π}{9}}{2^{3} s i n \frac{π}{9}}

=

\frac{s i n \frac{8 π}{9}}{8 s i n \frac{π}{9}}

=

\frac{s i n (π - \frac{π}{9})}{8 s i n \frac{π}{9}}

=

\frac{1}{8}

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