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.