Find the maximum area of an isosceles triangle inscribed in the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` with its vertex at one end of the major axis.

Explanation

To find the maximum area of an isosceles triangle inscribed in the ellipse given by the equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) with its vertex at one end of the major axis, we can follow these steps:

### Step 1: Understand the Geometry
The ellipse has its major axis along the x-axis and minor axis along the y-axis. The vertex of the triangle is at one end of the major axis, which we can take as the point \(A(a, 0)\).

### Step 2: Define the Other Vertices
Let the other two vertices of the triangle be \(B(-x, y)\) and \(C(x, y)\). Since the triangle is isosceles, the y-coordinates of points \(B\) and \(C\) are the same.

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