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

Question

Factor the expression and use the fundamental identities to simplify the expression

Answer 1

this is a version of a^2 + 2a + 1 = (a+1)^2 where a= tan^2x

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

tan^2x +1 = sec^2x