Question

The value of \( \csc^{2}\theta - \cot^{2}\theta \) is:

• A. \(1\)
• B. \(7\)
• C. \(49\)
• D. \(0\)

Hint:

Memorize \(\csc^{2}\theta = 1 + \cot^{2}\theta\) and \(\sec^{2}\theta = 1 + \tan^{2}\theta\). They help reduce many expressions instantly.

Answer 1

The Correct Option is A

Step 1: Recall the Pythagorean identity in trigonometry.
For any angle \(\theta\) (where defined), \(\;\csc^{2}\theta = 1 + \cot^{2}\theta.\)
Step 2: Substitute into the expression.
\[ \csc^{2}\theta - \cot^{2}\theta = (1 + \cot^{2}\theta) - \cot^{2}\theta = 1. \]
Step 3: Conclude.
Thus, the required value is \(1\).