Paradoja

¿La tangente es la unidad imaginaria?

¿Sabías que la tangente de cualquier ángulo es siempre la unidad imaginaria?

¿Cómo que no?

Síguenos en esta demostración y ya lo verás.

Todos sabemos que ((sen(x)) dx) puede ser escrito como (-d(cos(x))); también recordemos que ((cos(x)) dx) se puede escribir como (d(senx)).

Consideremos la siguiente integral:

Tomando en cuenta las consideraciones anteriores podemos escribir las siguientes igualdades:

Por lo tanto si resolvemos resulta:

Por consiguiente:

sen2(x) = -cos2(x)

De tal modo que si dividimos ambos miembros por cos2(x) resulta que:

tg2(x)=-1

Por consiguiente:

4.333335
Su voto: Nada Promedio: 4.3 (3 votos)

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...Por lo tanto, hay que examinar C1 y C2 para determinar lo que resulte de sen^(x) + cos^2(x). Pero como ya está demostrado para esta identidad, esa suma algebraica (de las constantes) DEBE dar 1. Por otra parte ¿es siempre válido dividir por cos^2(x)?... no olvidemos que cos(x) es función acotada entre -1 y 1, por lo tanto cos^2(x) podría valer CERO... es una restricción no contemplada al dividir por cos^2(x).

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Una observación

Observemos que cuando se llega a la igualdad sen^2(x) = -cos^2(x), podemos sumar a ambos miembros cos^2(x), con lo cual la ecuación queda sen^2(x) + cos^2(x) = 0. Como bien sabemos, existe una identidad trigonométrica (FUNDAMENTAL) que es sen^2(x) + cos^2(x) = 1, que aquí está siendo contradicha. Esto surge del hecho que, si bien es cierto, es correcta la igualdad entre ambas integrales, AMBAS SON INDEFINIDAS, y por lo tanto a ambas les falta en la solución, las correspondientes constantes (C1 y C2). Gracias por el espacio, y saludos.

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