How do you factor the expression and use the fundamental identities to simplify cos^2x+cos^2xtan^2x?

1 Answer
Jim G.
Feb 5, 2017

"simplifies to " 1

Explanation:

The required color(blue)"trigonometric identities" are.

color(red)(bar(ul(|color(white)(2/2)color(black)(1+tan^2x=sec^2x)color(white)(2/2)|)))

and color(red)(bar(ul(|color(white)(2/2)color(black)(secx=1/(cosx))color(white)(2/2)|)))

Taking out a common factor of cos^2x

rArrcos^2x(1+tan^2x)

Using the above identities.

=cos^2xsec^2x=cancel(cos^2x)^1xx1/(cancel(cos^2x)^1)=1

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