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

Question

Quizplus · Accepted Answer

The expression can be factored using the difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$, where $a = \tan^2x$ and $b = \sec^2x$. This gives $(\tan^2x - \sec^2x)(\tan^2x + \sec^2x)$. Since $\sec^2x = 1 + \tan^2x$, the expression simplifies to $-1(\tan^2x + 1) = -2\tan^2x - 1$.

Factor the Trigonometric Expression and Simplify tan⁡4x−sec⁡4x\tan ^ { 4 } x - \sec ^ { 4 } xtan4x−sec4x

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