work please, how did you get that?

### 4 Answers

There’s a trig identity that states:

1+tan^2 x=sec^2 x

We want to find what tan^2 x equals. To do this, subtract 1 from both sides.

tan^2 x=sec^2x-1

Now plug it into your expression:

(tan^4 x)+2(tan^2 x)+1=

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

(sec^2 x-1)(sec^2 x-1)+2(sec^2 x-1)+1

(sec^4 x)-2(sec^2 x)+1+2(sec^2 x-1+1

sec^4 x

tan^4(x) + 2tan^2(x) + 1 = (tan^2(x) + 1)^2 = (sec^2(x))^2 = sec^4(x)

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

= (tan^2x + 1)^2

= (sec^2x)^2

= sec^4x

sec^4 (x)