Perform the indicated operations and simplify the result so there are no quotients.
-$$\frac { 1 } { \cos ^ { 2 } \theta } - \frac { 1 } { \cot ^ { 2 } \theta }$$
A) $- \sec ^ { 2 } \theta$
B) $1 - \sin \theta$
C) 1
D) 0

Question

Quizplus · Accepted Answer

The expression can be rewritten using trigonometric identities: $\frac{1}{\cos^2 \theta} = \sec^2 \theta$ and $\frac{1}{\cot^2 \theta} = \tan^2 \theta$. Using the identity $\sec^2 \theta - \tan^2 \theta = 1$, the expression simplifies to 1.

Perform the Indicated Operations and Simplify the Result So There 1cos⁡2θ−1cot⁡2θ\frac { 1 } { \cos ^ { 2 } \theta } - \frac { 1 } { \cot ^ { 2 } \theta }cos2θ1​−cot2θ1​

Perform the Indicated Operations and Simplify the Result So There $\frac { 1 } { \cos ^ { 2 } \theta } - \frac { 1 } { \cot ^ { 2 } \theta }$