Question

Prove that $\sin x<x<\tan x\forall x\in (0,\pi /2)$.

Answer 1

Solution:

The blue line is for $y=\tan x$. The red line is for $y=x$ . The green line is for $y=\sin x$. As you can see, in the given interval the blue line is above the other two. So $\tan x$ is the greatest. The red line is in the middle while the green line is the lowest.

So $\sin x<x<\tan x$