To solve this equation, we can use the formula for the cosine of the sum of two angles:

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

Applying this formula to the given equation, we get:

cos(π/2 + x) cos(x) + sin(π/2 + x) sin(x) = 0

cos(π/2 + x) cos(x) + cos(π/2) sin(x) + sin(π/2) * cos(x) = 0

0 + 1 sin(x) + 1 cos(x) = 0

sin(x) + cos(x) = 0

Now, we can use the Pythagorean identity to simplify the equation further:

sin(x) = cos(x)

Now, we know that sin(x)/cos(x) = 1

So, x = π/4 + πn, where n is an integer.