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`
A. 6
B. 7
C. 8
D. 4

Answer 1

Correct Answer - B
We have,
`(1)/(sin((pi)/(n)))=(1)/(sin((2pi)/(n)))+(1)/(sin((3pi)/(n)))`
`implies (1)/(sin((pi)/(n)))-(1)/(sin((3pi)/(n)))=(1)/(sin((2pi)/(n)))`
`implies(sin((3pi)/(n))-sin((pi)/(n)))/(sin((pi)/(n))sin((3pi)/(n)))=(1)/(sin((2pi)/(n)))`
`implies(2sin((pi)/(n))cos((2pi)/(n)))/(sin((pi)/(n))sin((3pi)/(n)))=(1)/(sin((2pi)/(n)))`
`implies2sin((2pi)/(n))cos((2pi)/(n))=sin((3pi)/(n))`
`impliessin""(4pi)/(n)=sin""((3pi)/(n))implies(4pi)/(n)+(3pi)/(n)=piimpliesn=7`