Complete the identity.
-$\tan ^ { 4 } \theta - \sec ^ { 4 } \theta =$ ?
A) $- 2 \tan ^ { 2 } \theta - 1$
B) $\sec ^ { 2 } \theta + \tan ^ { 2 } \theta$
C) $\sec ^ { 2 } \theta$
D) $\tan ^ { 2 } \theta - \sec ^ { 2 } \theta$

Question

Quizplus · Accepted Answer

The identity can be derived by factoring and using the Pythagorean identity. $\tan^4\theta - \sec^4\theta = (\tan^2\theta)^2 - (\sec^2\theta)^2 = (\tan^2\theta + \sec^2\theta)(\tan^2\theta - \sec^2\theta)$. Since $\sec^2\theta = 1 + \tan^2\theta$, substituting this into the expression gives $(\tan^2\theta + (1 + \tan^2\theta))(\tan^2\theta - (1 + \tan^2\theta)) = (2\tan^2\theta + 1)(\tan^2\theta - 1 - \tan^2\theta) = -2\tan^2\theta - 1$.

Complete the Identity tan⁡4θ−sec⁡4θ=\tan ^ { 4 } \theta - \sec ^ { 4 } \theta =tan4θ−sec4θ=

Complete the Identity $\tan ^ { 4 } \theta - \sec ^ { 4 } \theta =$