Question #011db

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Answer 1 · 2017-04-27T01:20:12

Proved.

Given: $sec^2(x)/(sec^2(x)-1) =csc^2(x)$

Because $cos(x)sec(x) = 1$ , we shall multiply the the fraction by 1 in the form $cos^2(x)/cos^2(x)$ :

$cos^2(x)/cos^2(x)sec^2(x)/(sec^2(x)-1) =csc^2(x)$

This simplifies to the following:

$1/(1-cos^2(x)) =csc^2(x)$

We know that $1 - cos^2(x) = sin^2(x)$ :

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

We know that $csc^2(x) = 1/sin^2(x)$

$csc^2(x) =csc^2(x)$

Q.E.D.