If `x sin 45^(@) cos 45^(@) tan60^(@)=tan^(2)45^(@) -cos60^(@)`, then determine the value of x.

Explanation

`x sin 45^(@) cos 45^(@) tan60^(@) =tan^(2) 45^(@)-cos60^(@)`
or, `x xx (1)/(sqrt(2)) xx (1)/(sqrt(2))xx sqrt(3) = 1-(1)/(2)`
or, `x xx (sqrt(3))/(2) =1-(1)/(2) or, x xx (sqrt(3))/(2) =(1)/(2) or, x=(1)/(sqrt(3))`
Hence the required value of `x=(1)/(sqrt(3))`.