maxima & a wrong limit at infinity



Hello,

When I solve the following limit at infinity
 by Maxima ,the output is
infinity(-inf).

limit((2*sqrt((x/2+1)^2-(cos(29*%pi/360)*x/2)^2)
-x*sin(29*%pi/360))/
(%pi*cos(29*%pi/360)),x,inf);

To solve this limit, we?ll need the conjugate multiplication technique.
 I
multiplying the numerator and denominator 
by the conjugate of the numerator and
after simplification:

limit((4*x+4)/(%pi*cos(29*%pi/360)*
(2*sqrt(x^2/4+x+1-x^2/4*cos(29*%pi/360)^2)
+x*sin(29*%pi/360))),
x, inf);

Now, the output is correct. (=2.62)

Why the answer of the first limit was " infinity "? 
Why Maxima could not solve this limit correctly?

Thank you in advance.