Proof. Let x be an angle (in radians) between 0 and π/2. Recall that x is the length of the arc it subtends on the unit circle. The lengths of x, sin x, and tan x are as shown in the figure below.
These three quantities satisfy the inequatilities
Dividing each part of the equation above by sin x we obtain
As 
,
and the
term 
.
Hence
, as
and
, as
