Come si semplifica # sec ^ 4x-tan ^ 4x #?

#sec^4 x - tan^4 x = (sec^2 x - tan^2 x)(sec^2 x + tan^2 x)#
Dal
#(sec^2 x - tan^2 x) = [(1/(cos^2 x) - (sin^2 x/(cos^2 x))] = #
#= (1 - sin^2 x)/(cos^2 x) = cos^2 x/(cos^2 x) = 1#,
lì per;
#sec^4x - tan^4 x = sec^2 x + tan^2 x#
Promemoria: #sec^2 x = (1 + tan^2 x)#
Infine,
#sec^4 x - tan^4 x = 1 + 2tan^2 x#