Question

In \( \triangle ABC \), evaluate: \[ \cos A + \cos B + \cos C \]

• A. \( 1 + \frac{r}{2R} \)
• B. \( 1 - \frac{r}{R} \)
• C. \( 1 + \frac{R}{r} \)
• D. \( 1 + \frac{r}{R} \)

Hint:

In a triangle, \( \cos A + \cos B + \cos C = 1 + \frac{r}{R} \), where \( r \) is the inradius and \( R \) is the circumradius.

Answer 1

The Correct Option is D

Using the standard identity: \[ \cos A + \cos B + \cos C = 1 + \frac{r}{R} \] Thus, the correct answer is \( 1 + \frac{r}{R} \).