Question

Factor the expression and use the fundamental identities to simplify.
cos^2x + cos^2xtan^2x

Answer 1

\[\cos ^{2}x + \cos ^{2}xtan ^{2}x\]

Answer 2

The expression is equal to 1. Here how...

\[\cos^2x+\cos^2xtan^2x \]
\[\cos^2x(1+\tan^2x)\]
we know that \[1+\tan^2x=\sec^2x\]
therefore \[\cos^2x(\sec^2x)\]
but \[\sec^2x=1/\cos^2x\]
thus
\[\cos^2x(1/\cos^2x)\]
which equals 1

Answer 3

How did you get from cos2x+cos2xtan2x to cos2x(1+tan2x)?

Answer 4

since cos2x is in both terms you can factor it out giving you cos2x(1+tan2x) which is equal to the original equation if you multiply cos2x*(1+tan2x) you get (cos2x)(1)+(cos2x)(tan2x) which equals cos2x+cos2xtan2x

Answer 5

Oh! I see. Thanks so much, you've been a big help. :)