Question

Evaluate \( 9 \csc^2 22^\circ - 9 \cot^2 22^\circ + 1 = \):

• A. 9
• B. 10
• C. \( \frac{1}{9} \)
• D. 0

Hint:

Use the identity \( \csc^2 \theta = 1 + \cot^2 \theta \) to simplify expressions involving \( \csc^2 \theta \) and \( \cot^2 \theta \).

Answer 1

The Correct Option is D

We are given the expression \( 9 \csc^2 22^\circ - 9 \cot^2 22^\circ + 1 \). Using the identity \( \csc^2 \theta = 1 + \cot^2 \theta \), we can substitute into the expression: \[ 9 \csc^2 22^\circ = 9(1 + \cot^2 22^\circ) = 9 + 9 \cot^2 22^\circ. \] Thus, the expression becomes: \[ 9 + 9 \cot^2 22^\circ - 9 \cot^2 22^\circ + 1 = 9 + 1 = 10. \] Therefore, the value of the expression is \( \boxed{10} \).