Question

If \(\cos P = 1/7\) and \(\cos Q = 13/14\), where P and Q both are acute angles. Then the value of \(P - Q\) is

• A. 30°
• B. 60°
• C. 45°
• D. 75°

Hint:

\(\cos(P - Q) = 1/2 \rightarrow P - Q = 60°\) for acute angles.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Use \(\cos(P - Q) = \cos P \cos Q + \sin P \sin Q\).
Step 2: Detailed Explanation:
\(\sin P = \sqrt{1 - 1/49} = \sqrt{48}/7 = 4\sqrt{3}/7\)
\(\sin Q = \sqrt{1 - 169/196} = \sqrt{27}/14 = 3\sqrt{3}/14\)
\(\cos(P - Q) = (1/7)(13/14) + (4\sqrt{3}/7)(3\sqrt{3}/14) = 13/98 + 36/98 = 49/98 = 1/2\)
\(P - Q = 60°\)
Step 3: Final Answer:
\(P - Q = 60°\).