The tangent and the normal lines at the point `(sqrt3, 1)` to the circle `x^(2)+y^(2) = 4` and the X-axis form a triangle. The area of this triangle ( in square units ) is

Explanation

To find the area of the triangle formed by the tangent and normal lines at the point \((\sqrt{3}, 1)\) to the circle \(x^2 + y^2 = 4\) and the X-axis, we can follow these steps:

### Step 1: Identify the Circle and Point
The equation of the circle is \(x^2 + y^2 = 4\), which has a center at \((0, 0)\) and a radius of \(2\). The point given is \((\sqrt{3}, 1)\).

### Step 2: Find the Slope of the Tangent Line
To find the slope of the tangent line at the point \((\sqrt{3}, 1)\), we first differentiate the circle's equation implicitly:
\[
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