work please, how did you get that?
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.
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
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