Question

How do you factor the expression and use the fundamental identities to simplify `(tan^4x+2tan^2x+1)`?

Answer 1

`tan^4x+2tan^2x+1=sec^4x`

Explanation:

`tan^4x+2tan^2x+1`

i.e. `(tan^2x)^2+2xxtan^2x xx1+1^2`

i.e. `(tan^2x+1)^2` `color(red)(- as)->` `color(red)(a^2+2xxaxxb+b^2=(a+b)^2)`

i.e. `(sec^2x)^2` `color(red)(- as)->` `color(red)(tan^2x+1=sec^2x)`

i.e. `sec^4x`