Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $$\cot ^ { 2 } \alpha + \cot ^ { 2 } \alpha \cdot \tan ^ { 2 } \alpha$$
A) $\csc ^ { 2 } \alpha$
B) $1 + \cot ^ { 2 } \alpha$
C) $\sec ^ { 2 } \alpha$
D) $1 / \cos ^ { 2 } \left( \frac { \pi } { 2 } - \alpha \right)$
E) $\frac { 1 } { 1 - \cos ^ { 2 } \alpha }$

Question

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. ​​ $$\cot ^ { 2 } \alpha + \cot ^ { 2 } \alpha \cdot \tan ^ { 2 } \alpha$$
A)​ $\csc ^ { 2 } \alpha$
B)​ $1 + \cot ^ { 2 } \alpha$
C)​ $\sec ^ { 2 } \alpha$
D)​ $1 / \cos ^ { 2 } \left( \frac { \pi } { 2 } - \alpha \right)$
E)​ $\frac { 1 } { 1 - \cos ^ { 2 } \alpha }$

Quizplus · Accepted Answer

The expression simplifies to $\csc^2 \alpha$ using the identity $\cot^2 \alpha + 1 = \csc^2 \alpha$. Option C, $\sec^2 \alpha$, is not equivalent because it simplifies to $1/\cos^2 \alpha$, which is different from $1/\sin^2 \alpha$.

Factor;then Use Fundamental Identities to Simplify the Expression Below and Determine