Question

If \(\cos A = \frac{1}{7}\) and \(\cos B = \frac{13}{14}\), then \(\cos (A - B)\) is

• A. 1
• B. 13/98
• C. 1/2
• D. 18/49

Hint:

When using trigonometric identities, ensure you calculate \(\sin A\) and \(\sin B\) correctly when only the cosines are given.

Answer 1

The Correct Option is D

Use the formula for the cosine of the difference of two angles: \[ \cos (A - B) = \cos A \cos B + \sin A \sin B \] Substitute the values of \(\cos A = \frac{1}{7}\) and \(\cos B = \frac{13}{14}\), and calculate \(\sin A = \sqrt{1 - \cos^2 A}\) and \(\sin B = \sqrt{1 - \cos^2 B}\). After solving, we find: \[ \cos (A - B) = \frac{18}{49} \] Thus, the correct answer is \(18/49\).