sin-pi-7-sin-2pi-7-sin-3pi-7-

Question Number 89202 by jagoll last updated on 16/Apr/20

\sin (\frac{π}{7}) \sin (\frac{2 π}{7}) \sin (\frac{3 π}{7}) = ?

Commented by jagoll last updated on 16/Apr/20

w h e r e s i r ?

Commented by jdmath last updated on 16/Apr/20

D r . p e y a m v i d e o m a y b e h e l p f u l

Commented by jdmath last updated on 16/Apr/20

y o u t u b e \dots i w a s n t a b l e t o c o p y t h e l i n k . . s e a r c h i t

Commented by john santu last updated on 16/Apr/20

\underset{k = 2}{\prod^{n}} \sin (\frac{(k - 1) π}{n}) = \frac{n}{2^{n - 1}}

n = 7

\sin (\frac{π}{7}) \sin (\frac{2 π}{7}) \sin (\frac{3 π}{7}) \sin (\frac{4 π}{7})

\sin (\frac{5 π}{7}) \sin (\frac{6 π}{7}) = \frac{7}{64} \dots (i)

\sin (\frac{π}{7}) = \sin (\frac{6 π}{7})

\sin (\frac{2 π}{7}) = \sin (\frac{5 π}{7})

\sin (\frac{3 π}{7}) = \sin (\frac{4 π}{7})

{(\sin \frac{π}{7} \sin \frac{2 π}{7} \sin \frac{3 π}{7})}^{2} = \frac{7}{64}

\Rightarrow \sin \frac{π}{7} \sin \frac{2 π}{7} \sin \frac{3 π}{7} = \sqrt{\frac{7}{64}}

= \frac{\sqrt{7}}{8}