Question

If \(\cos A = 1/2\), then the value of \(\sin^2 A + \cos^2 A\) is :

• A. \(3/2\)
• B. \(5/4\)
• C. \(-1\)
• D. \(1/2\)

Hint:

This is a "trick" question. Don't waste time calculating the specific values of sine and cosine if you recognize a fundamental identity!

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The expression \(\sin^2 \theta + \cos^2 \theta\) is a fundamental trigonometric identity. It is constant for any valid angle \(\theta\).
Step 2: Key Formula or Approach:
Pythagorean Identity: \( \sin^2 \theta + \cos^2 \theta = 1 \) for any value of \(\theta\).
Step 3: Detailed Explanation:
1. The question provides \(\cos A = 1/2\). While we could find \(A = 60^\circ\) and then find \(\sin A\), it is unnecessary. 2. The identity \(\sin^2 A + \cos^2 A\) is independent of the value of \(A\). 3. Therefore, regardless of whether \(\cos A\) is \(1/2\), \(1/3\), or any other value, the sum of squares is always \(1/2\).
Step 4: Final Answer:
The value is \(1/2\).