Question

In \( \Delta ABC \), \( \left( \tan \frac{A}{2} + \tan \frac{B}{2} \right) \tan \frac{C}{2} = \):

• A. \( \frac{2c}{a + b + c} \)
• B. \( \frac{2c}{a + b - c} \)
• C. \( \frac{2c^2}{a^2 + b^2 + c^2} \)
• D. \( \frac{c}{a + b + c} \)

Hint:

For expressions involving half angles in triangles, use trigonometric identities and angle sum formulas to simplify.

Answer 1

The Correct Option is A

We are given the equation \( \left( \tan \frac{A}{2} + \tan \frac{B}{2} \right) \tan \frac{C}{2} \) in a triangle. By using standard trigonometric identities and simplifying, we find the value of the expression to be \( \frac{2c}{a + b + c} \).