Perform the indicated operations and simplify the result so there are no quotients.
-$\sec \theta - \frac { 1 } { \sec \theta }$
A) $\sin \theta \tan \theta$
B) $- 2 \tan ^ { 2 } \theta$
C) $\sec \theta \csc \theta$
D) $1 + \cot \theta$

Question

Quizplus · Accepted Answer

$\sec \theta - \frac { 1 } { \sec \theta }$ simplifies to $\sec \theta - \cos \theta$, which can be rewritten as $\frac{1}{\cos \theta} - \cos \theta$. Factoring this expression gives $\frac{1 - \cos^2 \theta}{\cos \theta}$, which simplifies to $\frac{\sin^2 \theta}{\cos \theta}$ due to the Pythagorean identity $1 - \cos^2 \theta = \sin^2 \theta$. This further simplifies to $\sin \theta \tan \theta$, matching choice A.

Perform the Indicated Operations and Simplify the Result So There sec⁡θ−1sec⁡θ\sec \theta - \frac { 1 } { \sec \theta }secθ−secθ1​

Perform the Indicated Operations and Simplify the Result So There $\sec \theta - \frac { 1 } { \sec \theta }$