¿Dónde radica el error?

Todos quienes hemos cursado algo de trigonometría en la escuela secundaria o en la Universidad podemos afirmar que...

cos²(α) = 1 – sen²(α); para todo ángulo α

por lo tanto:

(cos²(α))³ = (1 – sen²(α))³

tal que haciendo uso de la conmutatividad en la potencia de potencia resulta:

(cos³(α))² =(1 – sen²α)³

por consiguiente:

(cos³(α))² + 3 = √(1- sen²(α))³ + 3

si elevamos al cuadrado ambos miembros de la igualdad nos quedará:

(cos³(α))² + 6cos³(α) + 9 = (1 - sen²(α)³ + 6√(1 - sen²(α))³ + 3²

si cuando acordamos la propiedad la hicimos válida para todo ángulo es lícito, por ejemplo, considerar que α = π y todos sabemos que sen π = 0 mientras que cos π = -1, por consiguiente la última igualdad se transformará en:

((-1)³)² + 6.(-1)³ + 9 = (1-0)³ + 6.(1)³ + 9

o sea:

1 – 6 + 9 = 1 + 6 + 9

Por lo tanto

4 = 16

¡Es cuestión de buscar el error, si lo hay, y enviarnos tus descubrimientos!.

Su voto: Nada


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