Solve $\sec (x) + \tan (x) = 4$ $$\sec{x}+\tan{x}=4$$
Find $x$ for $0<x<2\pi$.
Eventually I get $$\cos x=\frac{8}{17}$$
$$x=61.9^{\circ}$$
The answer I obtained is the only answer, another respective value of $x$ in $4$-th quadrant does not solve the equation, how does this happen?  I have been facing the same problem every time I solved this kind of trigonometric equation.

The other answer you found is probably $\cos x = 0$ , which doesn't fit because in the original equation $\tan x$ can't be evaluated that way. Remember $tan x = \frac{\sin x}{ \ cos x}$
