How can this be reduced to the simplest form?

Question

#(sec^2x-1)/sec^2x#

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Answer 1 · 2018-03-08T17:30:06

#(sec^2 (x) -1)/(sec^2 (x)) = 1 - cos^2 (x) = sin^2 (x)#

Answer 2 · 2018-03-08T17:32:49

#sin^2x#

Using the Pythagorean and reciprocal identities:
#1+tan^2= sec^2x#
Therefore: #tan^2x= sec^2x-1#
#1/cos^2x= sec^2x#

#(sec^2x-1)/sec^2x=#

#(tan^2x)/sec^2x=#

#(sin^2x/cos^2x)/(1/cos^2x)=#

#(sin^2x/cancel(cos^2x))*cancel(cos^2x)/1=#

#sin^2x#