To find the possible values of "a" in the given equation cos(x) = -1 - a^2, we need to consider the range of the cosine function.

The cosine function has a range of -1 to 1. Since the right-hand side of the equation is -1 - a^2, we need to make sure that the expression falls within the valid range of the cosine function.

Since -1 - a^2 is on the left side of the equation, it needs to fall within the range of -1 to 1. This means that -1 - a^2 must be between -1 and 1 in order for the equation to hold true.

To satisfy this condition, we can set up the following inequality:

-1 < -1 - a^2 < 1

Solving the inequality, we get:

0 < a^2 < 2

Taking the square root of both sides, we get:

0 < a < √2

Therefore, the possible values of "a" that satisfy the given equation are all real numbers between 0 and the square root of 2.