Hi Maria,
First, observe that sec^2(x) = 1 + tan^2 (x).
Then substitute this for sec^2(x) in the formula:
sec^2(x) + tan(x) = 1
1 + tan^2(x) + tan(x) = 1
tan^2(x) + tan(x) = 0
tan(x)[tan(x) + 1] = 0
This allows us to set tan(x) = 0 and tan(x) + 1 = 0
The first part tells us that x = 0 + 2pi(n) where n is an integer as tan(0) = 0. That is, x can be 0, 2pi, 4pi, and so on.
The second part tells us that tan(x) = -1, that is, x = -pi/4 + 2pi(n) where n is an integer. So x = -pi/4, -pi/4 + 2p, and so on.
These are all the solutions for x given this equation. I hope this helps!
Rob
