How do you verify $(tan^2x)/(secx-1)-1=secx$ ?

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Answer 1 · 2015-07-22T11:55:45

$"Left Hand Side "= tan^2x/(secx-1)-1$

Use the identity : $cos^2x+sin^2x=1$
$=>1+tan^2x=sec^2x$
$=>tan^2x=sec^2x-1$

$=>"Left Hand Side "=(sec^2x-1)/(secx-1)-1=(cancel((secx-1))(secx+1))/cancel(secx-1)-1$

$=>secx+1-1=color(blue)secx= "Right Hand Side"$

How do you verify (tan^2x)/(secx-1)-1=secx(tan^2x)/(secx-1)-1=secx?