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

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Answer 1 · 2017-01-06T07:19:53

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

$tan^4x+2tan^2x+1$

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. $sec^4x$

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