To solve this equation, we need to use the trigonometric identity:

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

So, the equation becomes:

sin(-π/2 - x) = sin(-π/6)

Since sine function is an odd function, sin(-θ) = -sin(θ), so we can rewrite the equation as:

-sin(π/2 + x) = sin(-π/6)

Using the fact that sin(π/2 + x) = cos(x), the equation simplifies to:

-cos(x) = sin(-π/6)

Since sin(-π/6) = -1/2, the equation becomes:

-cos(x) = -1/2

Multiplying both sides by -1, we get:

cos(x) = 1/2

Therefore, x is equal to π/3 or 60 degrees.