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

The given question is about evaluating the expression \( \sin^2 A + \cos^2 A \) when \( \cos A = \frac{1}{2} \).

1. The trigonometric identity we use here is: \(\sin^2 A + \cos^2 A = 1\)
2. This identity holds true for any angle \( A \). It doesn't depend on the values of \( \sin A \) or \( \cos A \) specifically, as long as they represent the sine and cosine of the same angle.
3. According to this identity, the expression \( \sin^2 A + \cos^2 A \) will always equal 1, regardless of the value of \( \cos A \) or \( \sin A \).
4. Since we already established that the identity is always true, the correct value should be \( 1 \), not \( \frac{1}{2} \) as suggested by the "Correct Answer" section.

Therefore, despite the "Correct Answer" provided, according to trigonometric identities, the actual value of \(\sin^2 A + \cos^2 A\) is \(1\).

The value \(\frac{1}{2}\) given as a correct answer seems to be an error or misinterpretation.