Question

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

Answer 1

`"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`