Question 816078
verify the identity by showing that the left equals right 
sec^2x/1-tan^2=sec2x
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{{{sec^2(x)/(1-tan^2(x))=sec^2(x)}}}
start with left side:
{{{sec^2(x)/(1-tan^2(x))}}}
.. 
{{{(1/cos^2(x))/(1-(sin^2(x)/cos^2(x)))=(1/cos^2(x))/((cos^2(x)-sin^2(x))/cos^2(x))
=1/cos(2x)=sec(2x)}}}
..
verified: left side=right side