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Let's analyze the statements one by one to determine if they are true (V) or false (F):

**A.** En todo triángulo rectángulo el lado de menor longitud es la hipotenusa.
- **False (F):** In a right triangle, the hypotenuse is always the longest side, not the shortest.

**B.** El teorema de Pitágoras no puede cumplirse en un triángulo isósceles.
- **False (F):** The Pythagorean theorem applies to any right triangle, regardless of whether it is isosceles or not. An isosceles right triangle is a specific case where the two legs are equal.

**C.** En todo triángulo rectángulo, la suma de los cuadrados de las longitudes de los catetos es igual al cuadrado de la longitud de la hipotenusa.
- **True (V):** This statement correctly states the Pythagorean theorem, which is true for all right triangles.

**D.** El inverso del coseno del ángulo es la cosecante del ángulo.
- **False (F):** The inverse of the cosine function is the secant function, not the cosecant. The cosecant is the inverse of the sine function.

So, the correct answers are:
- **A: F**
- **B: F**
- **C: V**
- **D: F**

Would you like a more detailed explanation for any of these statements, or do you have any further questions? Here are some additional questions to explore:

1. Why is the hypotenuse always the longest side in a right triangle?
2. Can a triangle be both isosceles and right? If so, how?
3. How do you derive the Pythagorean theorem?
4. What are the definitions of secant and cosecant functions?
5. How do trigonometric identities relate to right triangles?

**Tip:** Remember that in trigonometry, understanding the relationships between functions like sine, cosine, and their reciprocals (cosecant, secant) is crucial for solving various problems.

Determine if the following statements are true (V) or false (F):
A. In every right triangle, the shortest side is the hypotenuse.
B. The Pythagorean theorem does not apply to an isosceles triangle.
C. In every right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
D. The reciprocal of the cosine of an angle is the cosecant of the angle.

Analyze the validity of statements related to right triangles, the Pythagorean theorem, and trigonometric functions. This problem explores key concepts in geometry and trigonometry, suitable for high school students in Grades 9-10.

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