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QUESTION
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##
