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

Options

A. `(-pi//8,pi//8)`
B. `(3pi//8,5pi//8)`
C. `(pi//4,3pi//4)`
D. `(7pi//8,9pi//8)`

Answer

A, B, D

Explanation

`(sin^(2)x+cos^(2)x)^(2)-3sin^(2)xcos^(2)xxx(sin^(2)x+cos^(2)x)gt(5)/(8)`
or `1-3sin^(2)xcos^(2)xgt(5)/(8)`
or `(3)/(8)gtsin^(2)xcos^(2)x`
`rArr 1-2cos^(2)2xgt0`
`rArr 4x in(-(pi)/(2),(pi)/(2))`
`n in Z`, generalizing now verify.