The value of the `(cos^(2)60^(@)+4sec^(2)30^(@)-tan^(2)45^(@))/(sin^(2)30^(@)+cos^(2)30^(@))`

Options

A. `(64)/(sqrt(3))`
B. `(55)/(12)`
C. `(67)/(12)`
D. `(67)/(10)`

Answer

b

Explanation

`(cos^(2)60^(@)+sec^(2)30^(@)-tan^(2)45^(@))/(sin^(2)30^(@)+cos^(@)30^(@))`
`rArr(((1)/(2))+4((2)/sqrt(3))^(2)-1)/( 1)`
`(sin^(2)A+cos^(2)A=1)`
`rArr(1)/(4)+(4xx4)/(3)-1 `
`rArr(1)/(4)+(16)/(3)-1`
`rArr(3+64-12)/(12)rArr( 55)/(12)`