How do you factor the expression and use the fundamental identities to simplify $tan^2x-tan^2xsin^2x$ ?

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Answer 1 · 2017-01-14T19:08:07

The answer is $sin^2x$

We use

$sin^2x+cos^2x=1$

$cos^2x=1-sin^2x$

$tanx=sinx/cosx$

Therefore,

$tan^2x-tan^2xsin^2x$

$=tan^2x(1-sin^2x)$

$=tan^2x*cos^2x$

$=sin^2x/cancel(cos^2x)*cancelcos^2x$

$=sin^2x$

How do you factor the expression and use the fundamental identities to simplify tan^2x-tan^2xsin^2xtan^2x-tan^2xsin^2x?