To solve this trigonometric equation, we first need to manipulate the equation so that it in terms of sine and cosine.

Using the identity sin(π/2 - x) = cos(x), we can rewrite the left side of the equation as:

2sin(π/2 - x/2) = 2cos(x/2)

Now, the equation becomes:

2cos(x/2) = 3cos(x/2) + 1

Subtracting 3cos(x/2) from both sides, we get:

2cos(x/2) - 3cos(x/2) = 1
-cos(x/2) = 1

Multiplying both sides by -1, we get:

cos(x/2) = -1

Since cosine is equal to -1 at π, we have:

x/2 = π
x = 2π

Therefore, the solution to the trigonometric equation 2sin(П/2-x/2)=3cos x/2+1 is x = 2π.