Write each expression in factored form as an algebraic expression of a single trigonometric function.
-$\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } x$
A) $4 \sec ^ { 2 } x$
B) $3 \sec ^ { 2 } x - 2$
C) $\sec ^ { 2 } x + 2$
D) $\tan ^ { 2 } x - 1$

Question

Quizplus · Accepted Answer

The expression can be factored using the trigonometric identity $\tan^2x = \sec^2x - 1$. Substituting this into the given expression yields $\sec^4x + \sec^2x(\sec^2x - 1) - 2(\sec^2x - 1)^2$. Simplifying this results in $3\sec^2x - 2$, which matches option B.

Write Each Expression in Factored Form as an Algebraic Expression sec⁡4x+sec⁡2xtan⁡2x−2tan⁡4x\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } xsec4x+sec2xtan2x−2tan4x

Write Each Expression in Factored Form as an Algebraic Expression $\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } x$