Show that `2 sin x + than x ge 3x all x in (0, pi/20).

Explanation

Let `f(x) = 2 sin x + tan x - 3x`
Then `f.(x) = 2 cos x + sec^2 x - 3`
Now `f.(x) gt 0 for all x in (0,pi/2)`.
Thus `f.(x) is increasing in (0,pi/2).
But `F(0) = 0`
Thus `f(x) ge 0 for all x in (0, pi/2)`
`rArr 2 sin x + tan x - 3x ge 0 for all x in (0, pi/2)cdot .
`2 sin x + tan x ge 3x for all x in (0,pi/2).