Question

Simplify (cot θ csc θ)² .

A. cot² θ csc² θ
B. cot² θ + csc² θ
C. cot² θ 2cot θ csc θ + csc² θ
D. cot² θ + 2cot θ csc θ + csc² θ

Answer 1

The expression (cot θ csc θ)² simplifies to cot² θ csc² θ, which matches option A in the original question.

Step-by-step explanation:

To simplify the expression (cot θ csc θ)² we need to apply the exponent to both trigonometric functions within the parentheses, yielding:

cot² θ csc² θ

This is because when an expression inside parentheses is raised to an exponent, the exponent applies to each term inside. So, the simplified form matches option A: cot² θ csc² θ.