Prove that $sec^2x/(sec^2x-1)=csc^2x$ ?

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Answer 1 · 2017-03-20T13:43:19

Please see below.

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

= $sec^2x/tan^2x$

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

= $1/cos^2x xx cos^2x/sin^2x$

= $1/cancel(cos^2x) xx cancel(cos^2x)/sin^2x$

= $1/sin^2x$

= $csc^2x$

Prove that sec^2x/(sec^2x-1)=csc^2xsec^2x/(sec^2x-1)=csc^2x?