Question 523103
Solve the equation on the interval 0< theta < 2pi 
sec^2theta+tan theta=0
**
using x in place of theta
sec^x+tanx=0
tan^2x+1+tanx=0
tan^2x+tanx+1=0
solve for tanx by quadratic formula:
..
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
..
a=1, b=1, c=1
&#8730;(b^2-4ac)=&#8730;(1-4)=&#8730;(-3)
Therefore, no real solution