To solve the trigonometric equation cos(x) + 1 = 0, we can first isolate the cosine term:

cos(x) = -1

Now, we know that the cosine function has a maximum value of 1 and a minimum value of -1. Therefore, the only time when cos(x) = -1 is when x = π.

So, the solution to the trigonometric equation cos(x) + 1 = 0 is x = π.