Question

If \(\alpha = \beta = 60^\circ\) then the value of \(\cos(\alpha - \beta)\) is

• A. \(\frac{1}{2}\)
• B. 1
• C. 0
• D. 2

Hint:

This problem is simpler than it looks. It's a basic substitution and evaluation question. Don't be confused by the angle subtraction formula for cosine; it's not needed here since the angles are equal.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We need to evaluate a trigonometric function by first substituting the given values for the angles.

Step 2: Key Formula or Approach:
First, calculate the value of the angle inside the cosine function, which is \((\alpha - \beta)\). Then, find the cosine of that resulting angle. We need to know the value of \(\cos 0^\circ\).

Step 3: Detailed Explanation:
We are given \(\alpha = 60^\circ\) and \(\beta = 60^\circ\).
Substitute these values into the expression \(\cos(\alpha - \beta)\):
\[ \cos(60^\circ - 60^\circ) \] \[ = \cos(0^\circ) \] The value of \(\cos 0^\circ\) is a standard trigonometric value.
\[ \cos 0^\circ = 1 \]

Step 4: Final Answer:
The value of \(\cos(\alpha - \beta)\) is 1.