If `x sin 60^(@) cos^(2)30^(@) =(tan^(2)45^(@) sec60^(@))/("cosec"60^(@))`, then find the value of x.

Explanation

Given that `x sin 60^(@) cos^(2)30^(@)=(tan^(2) 45^(@) sec 60^(@))/("cosec"60^(@))`
`or, x xx (sqrt(3))/(2) xx ((sqrt(3))/(2))^(2) =((1)^(2) xx 2)/((2)/(sqrt(3)))`
`or, x xx (sqrt(3))/(2) xx (3)/(4) =(2sqrt(3))/(2) or, x=(8)/(3) =2(2)/(3)`
Hence the value of `x=2(2)/(3)`.