To solve this equation, we can expand the left side and simplify.

(Sin x/2 - cos x/2)^2
= (sin^2(x/2) - 2sin(x/2)cos(x/2) + cos^2(x/2))
= sin^2(x/2) + cos^2(x/2) - 2sin(x/2)cos(x/2)
= 1 - 2sin(x/2)cos(x/2)

Now we have:

1 - 2sin(x/2)cos(x/2) = -1/2

Multiplying by 2 to get rid of the fraction:

2 - 4sin(x/2)cos(x/2) = -1

Rearranging:

4sin(x/2)cos(x/2) = 3

sin(x) = 2(2sin(x/2)cos(x/2))

Using the double angle formula for sine:

sin(x) = 2sin(x/2)cos(x/2)

Since sin(x) = 2sin(x/2)cos(x/2), we see that sin(x) = sin(x). Therefore, this equation holds true for all values of x.