**Solution:**

To determine the region formed by the points whose coordinates satisfy the given expression, we need to analyze each term separately and then combine the conditions to find the common region.

**Analyzing the first term: (2cos t)**

Since cosine function oscillates between -1 and 1, the value of 2cos t can vary from -2 to 2. For the given expression to be positive, the value of 2cos t must be greater than 0. Therefore, -2 < 2cos="" t="" />< />

**Analyzing the second term: (1/2 cos x cos y)**

Since cosine function oscillates between -1 and 1, the value of 1/2 cos x cos y can vary from -1/2 to 1/2. For the given expression to be positive, the value of 1/2 cos x cos y must be greater than 0. Therefore, -1/2 < 1/2="" cos="" x="" cos="" y="" />< />

**Analyzing the third term: (cos x cos y)**

Since cosine function oscillates between -1 and 1, the value of cos x cos y can vary from -1 to 1. For the given expression to be positive, the value of cos x cos y must be greater than 0. Therefore, -1 < cos="" x="" cos="" y="" />< />

**Analyzing the fourth term: (1)**

The value of 1 is always positive, so it does not contribute any conditions to the given expression.

**Analyzing the fifth term: (cos x - cos y)**

Since cosine function oscillates between -1 and 1, the value of cos x - cos y can vary from -2 to 2. For the given expression to be positive, the value of cos x - cos y must be greater than 0. Therefore, -2 < cos="" x="" -="" cos="" y="" />< />

**Analyzing the sixth term: (cos 2t)**

Since cosine function oscillates between -1 and 1, the value of cos 2t can vary from -1 to 1. For the given expression to be positive, the value of cos 2t must be greater than 0. Therefore, -1 < cos="" 2t="" />< />

**Combining the conditions:**

By analyzing each term separately, we have obtained the following conditions for the given expression to be positive:
- -2 < 2cos="" t="" />< />
- -1/2 < 1/2="" cos="" x="" cos="" y="" />< />
- -1 < cos="" x="" cos="" y="" />< />
- -2 < cos="" x="" -="" cos="" y="" />< />
- -1 < cos="" 2t="" />< />

To find the common region satisfying all these conditions, we need to intersect the intervals obtained from each condition.

The common region will be the intersection of the intervals (-2, 2), (-1/2, 1/2), (-1, 1), (-2, 2), and (-1, 1), which is (-1/2, 1/2).

Therefore, the points whose coordinates (X, y) satisfy the given expression and form the region in the coordinate plane are the points lying between the lines X = -1/2 and X = 1/2.