Use an identity to write the expression as a single trigonometric function or as a single number.
-$\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } x$
A) $\tan ^ { 2 } x - 1$
B) $3 \sec ^ { 2 } x - 2$
C) $4 \sec ^ { 2 } x$
D) $\sec ^ { 2 } x + 2$

Question

Quizplus · Accepted Answer

Using the trigonometric identity $\tan^2x = \sec^2x - 1$, the expression can be simplified as follows: $\sec^4x + \sec^2x(\sec^2x - 1) - 2(\sec^2x - 1)^2$. Simplifying this expression leads to $3\sec^2x - 2$.

Use an Identity to Write the Expression as a Single sec⁡4x+sec⁡2xtan⁡2x−2tan⁡4x\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } xsec4x+sec2xtan2x−2tan4x

Use an Identity to Write the Expression as a Single $\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } x$