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#