Question

\(cos(cos^{-1}(-\frac{1}{2})+\frac{π}{3}) =\)

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

Hint:

arccos(-1/2) is 2pi/3, so the angle becomes pi.

Answer 1

The Correct Option is B

Step 1: Use the addition formula:
Let $\alpha = \cos^{-1}(-\tfrac12)$, so $\cos\alpha = -\tfrac12$ and $\sin\alpha = \tfrac{\sqrt3}{2}$.

Step 2: Expand:
$\cos(\alpha + \tfrac\pi3) = \cos\alpha\cos\tfrac\pi3 - \sin\alpha\sin\tfrac\pi3 = -\tfrac14 - \tfrac34$.

Step 3: Result:
The value is $-1$, option (B).

Final Answer:
The value is -1. \[ \boxed{\text{(B) }-1} \]