ricorda:
tan^2(α) = sen^2(α) /cos^2(α);
sen^2(α) + cos^2(α) = 1
1 + [1/cos^2(α)] + [sen^2(α) /cos^2(α)] - [1/ sen^2(α) * sen^2(α) /cos^2(α)] =
= 1 + [1/cos^2(α)] + sen^2(α) /cos^2(α) - 1 / cos^2(α) =
mcd = cos^2(α);
= cos^2(α) / cos^2(α) + 1 / cos^2(α) + sen^2(α) / cos^2(α) - 1 / cos^2(α) =
= [cos^2(α) + 1 + sen^2(α) - 1] / cos^2(α) =
= [ cos^2(α) + sen^2(α) ] / cos^2(α) = 1 / cos^2(α).
Ciao. @franciusca