Question

The positive integer value of `n >3` satisfying the equation `1/(sin(pi/n))=1/(sin((2pi)/n))+1/(sin((3pi)/n))i s`

Answer 1

Correct Answer - 7
`(1)/(sin""(pi)/(n)) - (1)/(sin ""(3pi)/(n))= (1)/(sin""(2pi)/(n))`
or `" "(sin""(3pi)/(n)- sin""(pi)/(n))/(sin ""(pi)/(n)sin ""(3pi)/(n)) = (1)/( sin ""(2pi)/(n))`
or `((2sin""(pi)/(n) cos""(2pi)/(n)) sin""(2pi)/(n))/(sin ""(pi)/(n)sin ""(3pi)/(n)) =1`
or `sin ""(4pi)/(n) = sin "(3pi)/(n)`
`rArr (4pi)/(n) + (3pi)/(n) =pi`
`rArr n =7`.