Question

The value of \[ \frac{1}{2} \cos^{-1} \left( \cos \left( \frac{\pi}{3} - \frac{\sqrt{63}}{8} \right) \right) \] is

• A. \( 3/16 \)
• B. \( 3/8 \)
• C. 3/4
• D. \( 1/8 \)

Hint:

For expressions involving inverse trigonometric functions, use trigonometric identities to simplify before evaluating.

Answer 1

The Correct Option is C

Step 1: Simplify the expression.
Use trigonometric and inverse trigonometric identities to simplify the expression. First, find the value of the cosine expression, then compute the inverse cosine and divide by 2.
Step 2: Conclusion.
The value of the expression is \( 3/4 \). Final Answer: \[ \boxed{\frac{3}{4}} \]