In which of the following sets the inequality `sin^6x+cos^6x >5/8` holds good? (a)`(-pi/3,pi/8)` (b) `((3pi)/8,(5pi)/8)` (c) `(pi/4,(3pi)/4)` (d) `((7pi)/8,(9pi)/8)`

Explanation

`sin^6x+cos^6x gt 5/8`

`=>(sin^2x)^3+(cos^2x)^3 gt 5/8`

`=>(sin^2x+cos^2x)^3 - 3sin^2xcos^2x(sin^2x+cos^2x) gt 5/8`

`=>1-3sin^2xsin^2x gt 5/8`

`=>3sin^2xcos^2x lt 3/8`

`=>8sin^2xcos^2x lt 1`

`=>2sin^2 2x lt 1`

`=>1-2sin^2 2x gt 0 `

...