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

Question

Quizplus · Accepted Answer

The expression can be factored using the identity $\sec^2x = 1 + \tan^2x$. Rewrite $\sec^4x$ as $(\sec^2x)^2$ and $\tan^4x$ as $(\tan^2x)^2$, then factor using the difference of squares: $\tan^4x - \sec^4x = (\tan^2x)^2 - (\sec^2x)^2 = (\tan^2x + \sec^2x)(\tan^2x - \sec^2x)$. Using the identity $\sec^2x = 1 + \tan^2x$, we simplify to get $-2\tan^2x - 1$.

Write Each Expression in Factored Form as an Algebraic Expression tan⁡4x−sec⁡4x\tan ^ { 4 } x - \sec ^ { 4 } xtan4x−sec4x

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