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(sec^2x+tan^2x)^2 / sec^4x-tan^4x = sec^2 x+tan^2x
(sec^2x+tan^2x)^2 / sec^4x-tan^4x = sec^2 x+tan^2x
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Factorizacion
Diferencia de cuadrados
a² - b² = (a + b)(a - b)
(Sec²x + tan²x)²
-------------------- = sec²x + tan²x
sec⁴x - tan⁴x
(sec²x + tan²)(sec²x + tan²x)
--------------------------------------- -= sec²x + tan²x Simplificas
(sec²x + tan²x)(sec²x - tan²x)
sec²x + tan²x
------------------- = sec²x + tan²x (por identidad fundamental
sec²x - tan²x sec²x - tan²x = 1)
sec²x + tan²x
------------------- = sec²x + tan²x
1
Sec²x + tan²x = sec²x + tan²x