Solve the inequality `sin2x gtsqrt(2)sin^2x+(2-sqrt(2))cos^2x`

Answer

`x in (n pi +pi/8, n pi+pi/4), n in Z`

Explanation

`sin 2x gt sqrt(2) sin^(2) x+(2 -sqrt(2)) cos^(2)x`
`rArr 2 sin x cos x gt sqrt(2) sin^(2) x+(2-sqrt(2))cos^(2) x`
`rArr tan^(2)x-sqrt(2) tan x+(sqrt(2)-1) lt 0`
`rArr (tan x-1) (tan x-(sqrt(2)-1)) lt 0`
`rArr (sqrt(2)-1) lt tan x lt 1`
`rArr pi//8 lt x lt pi//4`
`:. x in (n pi + pi/8, n pi +pi/4)` where `n in Z`.