Trig Equation

What do we know about tan(x) and sec(x)? We know $\tan(x)=\frac{\sin(x)}{\cos(x)}, sec(x)=\frac{1}{cos(x)}$. Now use these, and replace them in the equation. 

We get $\frac{sin(x)}{\cos(x)}+\frac{1}{cos(x)}=0$. Multiplying by cos(x), with the restriction, cos(x) is not equal to 0, gives us $\sin(x)+1=0$, or $sin(x)=-1$. So, now we use the formula, ${\sin}^{2}(x)+{\cos}^{2}(x)=1$, we get $cos^2(x)=0, cos(x)=0$. Notice there is only one solution, because +/- 0 is always 0.

But we see from ealier that cos(x) is not 0, so we have no solution.