Question 1134558
.
<pre>
Given  x = {{{a*tan(theta)}}}.


Then  {{{1 + x^2/a^2)}}} = {{{1 + (a^2*tan^2(theta))/a^2}}} = {{{1 + tan^2(theta)}}} = {{{1 + sin^2(theta)/cos^2(theta)}}} = {{{(cos^2(theta) + sin^2(theta))/cos^2(theta)}}} = {{{1/cos^2(theta)}}}.


Therefore,  {{{sqrt(1 + x^2/a^2)}}} = {{{sqrt(1/cos^2(theta))}}} = {{{1/cos(theta)}}}.


The sign of the resulting expression follows the sign of {{{cos(theta)}}} in its quadrant.
</pre>