The value of `((1)/(3)cos30^(@))/((1)/(2)sin45^(@))+(tan60^(@))/(cos30^(@))=`

Options

A. `(6+sqrt(6))/(3)`
B. `(6-sqrt(6))/(sqrt(3))`
C. `(6-sqrt(6))/(3)`
D. `(6-sqrt(6))/(3)`

Explanation

`((1)/(3)cos 30^(@))/((1)/(2)sin45^(@)) + (tan60^(@))/(cos30^(@)) =((1)/(3)xx(sqrt(3))/(2))/((1)/(2)xx(1)/(sqrt(2)))+(sqrt(3))/((sqrt(3))/(2))=((1)/(2sqrt(3)))/((1)/(2sqrt(2)))+sqrt(3)xx (2)/(sqrt(3))`
` =(1)/(2sqrt(3))xx(2sqrt(2))/(1) +2=(sqrt(2))/(sqrt(3))+2=(sqrt(2)+sqrt(3))/(sqrt(3)+sqrt(3))+2`
`=(sqrt(6))/(3)+2=(sqrt(6)+6)/(3)=(6+sqrt(6))/(3)`
`therefore` (c ) is correct.