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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##