You can put this solution on YOUR website! establish each identity
sec(2 theta)= sec^2 theta over 2- sec^2 theta
use x for theta
sec2x=sec^2x/(2-sec^2x)
start with right side
sec^2x/(2-sec^2x)
=1/cos^2x/(2-(1/cos^2x))
=1/cos^2x/[(2cos^2x-1)/cos^2x]
cancel out cos^2x
=1/(2cos^2x-1)
=1/(2(1-sin^2x)-1)
=1/(2-2sin^2x-1)
=1/1-2sin^2x
=1/cos2x
=sec2x
verified: right side=left side
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