`(x-xtan^(2)30^(@))/(1+tan^(2)30^(@))=Sin30^(2)30^(@)+4 Cot^(2)45^(@)-Sec^(2)60^(@)`
Then value of x is

Options

A. `(1)/(4)`
B. `(1)/(sqrt3)`
C. `(1)/(2)`
D. `(1)/(5)`

Answer

c

Explanation

`(x-xtan^(3)30^(@))/(1xxtan^(3)30^(@))`
`=sin^(3)30^(@)+4cot^(2)45^(@)-sec^(2)60^(@)`
`(x(1-tan^(3)30^(@)))/(1+tan^(3)30^(@))=((1)/(2))^(2)+4xx1=(2)^(2)`
`x[1-((1)/sqrt(3))^(2)]`
`1+((1)/sqrt(3))^(2)=(1)/(4)+4-4`
`1+((1)/sqrt(3))^(2)=(1)/(4)+4 -4`
`(x[1-(1)/(3)])/(1+(1)/(3))=(1)/(4)`
`x xx(2)/(3)=(1)/(4)xx(4)/(3)`
`x=(1)/(3)xx(3)/(2)=(1)/(2)`