If `tan""(2pi)/(18),x andtan""(7pi)/(18)` are in A.P. and `tan""(2pi)/(18),t and tan""(5n)/(18)` are in A.P. then the value of `x/y` will be

Options

A. `1//2`
B. 2
C. 1
D. none of these

Answer

B

Explanation

It is given that
`tan""(2pi)/(18),x, tan ""(7pi)/(18)` are in A.P.
Also, `tan""(2pi)/(18),y, tan""(7pi)/(18)` are in A.P.
`therefore2x=tan""(2pi)/(18)+tan""(7pi)/(18)and2y=tan""(2pi)/(18)+tan""(5pi)/(18)`
`implies2x=tan20^(@)+tan70^(@)and 2y=tan20^(@)+tan50^(@)`
`implies2x=(1)/(sin20^(@)cos20^(@))and 2y =(sin70^(@))/(cos20^(@)cos50^(@))`
`implies2x=(1)/(sin20^(@)cos20^(@))and2y=(1)/(cos50^(@))`
`impliesx=(1)/(sin40^(@))and2y=(1)/(sin40^(@))`
`impliesx=2yimpliesx/y=2`