Question

The value of `sinpi/(14)sin(3pi)/(14)sin(5pi)/(14)sin(7pi)/(14)sin(9pi)/(14)sin(11pi)/(14)sin(13pi)/(14)` is equal to___________

Answer 1

`sintheta=sin(pi-theta)`
`sin(9/14pi)=sin(pi-9/14pi)=sin5/14pi`
`sin11/14pi=sin3/14pi`
`sin13/14pi=sinpi/14`
`=sin^2pi/14sin^2 3/14pisin^2 5/14pi`
`=(sinpi/14sin3/14pisin5/14pi)^2`
`1/(4sin^2pi/7)[sin2/7pisoc2/7pi*cos(pi-4/7pi)]^2`
`1/(16sin^2pi/7)[1/4sin^28/7pi]`
`1/64*(sin^2(pi+pi/7)/(sin^2pi/7))`
`1/64*sin^2(pi/7)/sin^2(pi/7)`
`1/64`.