For ` x in (0,(pi)/(2))` prove that `"sin"^(2) x lt x^(2) lt " tan"^(2) x`

Explanation

`"Let " f(x) =x^(2) -sin^(2) x`
`=(x +sinx) (x -sinx) gt0`
`" for " x in (0,(pi)/(2)) rArr " "sin^(2) x lt x^(2) " ".......(i)`
`"Let " g (x) =x^(2) -"tan"^(2) x`
` =(x + tan x) (x +tan x) lt 0 `
`" for " x in (0,(pi)/(2)) rArr " " x^(2) lt tan^(2) x " ".......(ii)`
From (i) & (ii) `sin^(2) x lt x^(2) lt tab^(2) x`