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sin ""(pi)/(14).sin""(3pi)/(14).sin""(5p...

`sin ""(pi)/(14).sin""(3pi)/(14).sin""(5pi)/(14).sin""(7pi)/(14).sin""(9pi)/(14).sin""(11pi)/(14).sin""(13pi)/(14)=`

A

`1//64`

B

`3//64`

C

`5//64`

D

`7//64`

Text Solution

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The correct Answer is:
A
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If sin""(pi)/18 sin""(5pi)/18 sin""(7pi)/18 =

sin""(3pi)/(5)+ sin""(4pi)/5+sin""(6pi)/(5)+sin""(7pi)/(5)=

"sin"pi/14" sin"(3pi)/14" sin"(5pi)/14" sin"(7pi)/5=

sin(pi/10)sin((13pi)/10)=

sin^(2)""(pi)/(18)+sin^(2)""(2pi)/(18)+sin^(2)""(4pi)/(18)+sin^(2)""(8pi)/(18)+sin^(2)""(7pi)/(18)+sin^(2)""(5pi)/(18)=

Show that sin""(pi)/5.sin""(2pi)/5.sin""(3pi)/5.sin""(4pi)/5=5/16 .

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