Wie vereinfacht man # (sec ^ 2x) - (tan ^ 2x) #?

Beachten Sie, dass:

#sin^2 x + cos^2 x = 1#

Daher:

#cos^2 x = 1 - sin^2 x#

und wir finden:

#sec^2 x - tan^2 x = 1/cos^2 x - sin^2 x/cos^2 x#

#color(white)(sec^2 x - tan^2 x) = (1 - sin^2 x)/cos^2 x#

#color(white)(sec^2 x - tan^2 x) = cos^2 x/cos^2 x#

#color(white)(sec^2 x - tan^2 x) = 1#