To find the value of \(P - Q\), given that both \(P\) and \(Q\) are acute angles and \(\cos P = \frac{1}{7}\) and \(\cos Q = \frac{13}{14}\), we proceed as follows:
- Since \(P\) and \(Q\) are acute angles, their cosine values must be positive and less than or equal to 1. The angles must also lie between 0° and 90°.
- Determine \(P: \cos^{-1}(\frac{1}{7})\).
- Using a calculator or trigonometric table, find the angle whose cosine is \(\frac{1}{7}\).
- Determine \(Q: \cos^{-1}(\frac{13}{14})\).
- Similar to step 2, find the angle whose cosine is \(\frac{13}{14}\).
- Calculate \(P - Q\).
- Since this involves inverse trigonometric functions, precise values can be computed using a calculator.
- By calculation or lookup, find \(\cos^{-1}(\frac{1}{7}) \approx 81.8°\) and \(\cos^{-1}(\frac{13}{14}) \approx 21.8°\).
- Then, compute \(P - Q = 81.8° - 21.8° = 60°\).
- Verify the correct answer: The computation yields \(P - Q = 60°\), which matches the given correct answer option.
Hence, the value of \(P - Q\) is \(60^\circ\).