the least positive value of x satisfying `( sin^(2) 2x + 4 sin^(4) x - 4 sin^(2) x cos^(2) x )/( 4-sin^(2) 2x- 4 sin^(2) x) = 1/9` is

Explanation

`(sin^2 2x+4sin^4x - 4sin^2xcos^2x)/4 = 1/9`

`=>((2sinxcosx)^2+4sin^4x - 4sin^2xcos^2x)/4 = 1/9`

`=>(4sin^2xcos^2x+4sin^4x - 4sin^2xcos^2x)/4 = 1/9`

`=>(4sin^4x)/4 = 1/9`

`=>sin^4x = 1/9`

`=>sinx = +-1/sqrt3`

So, least positive value of `x` will be `sin^-1(1/sqrt3).`