How do you simplify $(sec y - tan y) (sec y + tan y) / sec y$ ?

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Answer 1 · 2016-06-09T00:12:28

Apply the identity $sectheta = 1/costheta$ and $tantheta = sintheta/costheta$ .

$1/cosy - siny/cosy((1/cosy + siny/cosy)/(1/cosy))$

$=((1 - siny)(1 + siny)/cosy)/(cancel(cosy) xx 1/cancel(cosy))$

$= (1 - sin^2y)/cosy$

Apply the pythagorean identity $cos^2theta = 1 - sin^2theta$

$= cos^2y/cosy$

$=cosy$

Hopefully this helps!

Answer 2 · 2016-06-09T05:50:37

$cosy$

Given expression
$=((secy-tany)(secy+tany))/secy$

$=(sec^2y-tan^2y)*cosy$
$=1*cosy=cosy$
[Using formula $(sec^2y-tan^2y)=1 and 1/secy=cosy$ ]

How do you simplify (sec y - tan y) (sec y + tan y) / sec y (sec y - tan y) (sec y + tan y) / sec y?