Solve $\frac{\cos x}{1+\sin x} + \frac{1+\sin x}{\cos x} = 2$ I am fairly good at solving trig equations yet this one equation has me stumped. I've been trying very hard but was unable to solve it. Can anyone help please? Thank you.
$$\frac{\cos x}{1+\sin x} + \frac{1+\sin x}{\cos x} = 2$$
solve for $x$ in the range of $[-2\pi, 2\pi]$
I do know we have to do a difference of squares, yet after that, I don't know what to do and I get lost.
Thank you.

Hint:  if you put the two fractions over a common denominator you get a nice cancellation.
