How do you simplify (sec^2x) – (tan^2x)?

##sec^2 x – tan^2 x = 1##
Note that:
##sin^2 x + cos^2 x = 1##
Hence:
##cos^2 x = 1 – sin^2 x##
and we find:
##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##