Prove that $2\sin x+\tan x \geq 3x,\quad 0 < x< \frac{\pi}{2}$
Trial: $2\sin x+\tan x \geq 3x\equiv 2\sin x+\tan x -3x\geq 0$. So, let $f(x)=2\sin x+\tan x-3x$.Here $f(0)=0$ and If I can show $f'(x) \geq 0,\forall x \in (0,\frac{\pi}{2})$, then I can prove the inequality. Now $f'(x)=2\cos x + \sec^2x-3$.How to show $f'(x) \geq 0$. Please help.