Evaluate the following expression.
$3 \sec ^ { 2 } y - 3 \cot ^ { 2 } \left( \frac { \pi } { 2 } - y \right)$
A)0
B)- 3
C)4
D)- 4
E)3

Name: Evaluate the following expression. $3 \sec ^ { 2 } y - 3 \cot ^ { 2 } \left( \frac { \pi } { 2 } - y \right)$ A)0 B)- 3 C)4 D)- 4 E)3
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Question

Evaluate the following expression. 
 $3 \sec ^ { 2 } y - 3 \cot ^ { 2 } \left( \frac { \pi } { 2 } - y \right)$  
A)0
B)- 3
C)4
D)- 4
E)3

Quizplus · Accepted Answer

The expression simplifies to $3 \sec^2 y - 3 \tan^2 y$ because $\cot(\frac{\pi}{2} - y) = \tan y$. Using the identity $\sec^2 y = 1 + \tan^2 y$, the expression becomes $3(1 + \tan^2 y) - 3 \tan^2 y = 3$.

Evaluate the Following Expression 3sec⁡2y−3cot⁡2(π2−y)3 \sec ^ { 2 } y - 3 \cot ^ { 2 } \left( \frac { \pi } { 2 } - y \right)3sec2y−3cot2(2π​−y)

Evaluate the Following Expression $3 \sec ^ { 2 } y - 3 \cot ^ { 2 } \left( \frac { \pi } { 2 } - y \right)$