Factor the trigonometric expression and simplify.
-$\sec ^ { 4 } x - 2 \sec ^ { 2 } x \tan ^ { 2 } x + \tan ^ { 4 } x$
A) 1
B) $\sec ^ { 2 } x \left( 1 + \tan ^ { 2 } x \right)$
C) 2
D) $\sec ^ { 2 } x + \tan ^ { 2 } x$

Question

Quizplus · Accepted Answer

This expression can be recognized as a perfect square trinomial, factoring to $(\sec^2 x - \tan^2 x)^2$. Using the trigonometric identity $\sec^2 x = 1 + \tan^2 x$, the expression simplifies to $(1)^2$, which is 1.

Factor the Trigonometric Expression and Simplify sec⁡4x−2sec⁡2xtan⁡2x+tan⁡4x\sec ^ { 4 } x - 2 \sec ^ { 2 } x \tan ^ { 2 } x + \tan ^ { 4 } xsec4x−2sec2xtan2x+tan4x

Factor the Trigonometric Expression and Simplify $\sec ^ { 4 } x - 2 \sec ^ { 2 } x \tan ^ { 2 } x + \tan ^ { 4 } x$