Question 1029359
{{{3/secx + 2secx + 5 = 0}}}

==> {{{(3+2sec^2(x) + 5secx)/secx = 0}}}

==> {{{((2secx +3)(secx + 1))/secx = 0}}}

Assuming {{{secx <> 0}}}, we get 

secx = -3/2, or   secx = -1

==> {{{tan^2(x) + 1 = 9/4}}}, or {{{tan^2(x) + 1 = 1}}}.

==> {{{tan^2(x)= 5/4}}}, or {{{tan^2(x) = 0}}}.

Incidentally, when the value of tangent squared is 5/4 or 0, {{{secx<>0}}}, hence these are the two valid values for {{{tan^2(x)}}}.