Question

In a \( \triangle ABC \), \( A - B = 120^\circ \), \( R = 8r \), then \[ \frac{1 + \cos C}{1 - \cos C} =\ ? \]

• A. 16
• B. 14
• C. 15
• D. 10

Hint:

When a relation between angles is given, try expressing unknown angles or sides in terms of each other and use known identities involving circumradius \( R \) and inradius \( r \).

Answer 1

The Correct Option is C

Given: - \( A - B = 120^\circ \) - \( R = 8r \) We are asked to find: \[ \frac{1 + \cos C}{1 - \cos C} \] Using known trigonometric and geometric identities in a triangle, and substituting appropriate values based on the given relationships, the evaluated expression yields: \[ \frac{1 + \cos C}{1 - \cos C} = 15 \]