Question

\(1 + \cot^2 \theta = \)

• A. \(\sin^2 \theta\)
• B. \(\csc^2 \theta\)
• C. \(\tan^2 \theta\)
• D. \(\sec^2 \theta\)

Hint:

Memorizing the three Pythagorean identities is absolutely essential for trigonometry. They are used frequently for simplifying expressions and proving other identities.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question asks for one of the fundamental Pythagorean identities in trigonometry.

Step 2: Key Formula or Approach:
The three Pythagorean identities are:
1. \(\sin^2 \theta + \cos^2 \theta = 1\)
2. \(1 + \tan^2 \theta = \sec^2 \theta\)
3. \(1 + \cot^2 \theta = \csc^2 \theta\)

Step 3: Detailed Explanation:
The expression given is \(1 + \cot^2 \theta\). By direct application of the third Pythagorean identity, this is equal to \(\csc^2 \theta\).

Step 4: Final Answer:
The expression \(1 + \cot^2 \theta\) is equal to \(\csc^2 \theta\).