1. What is the Tan (A+B)/2 Formula?

The formula \(\tan\left(\frac{A+B}{2}\right) = \frac{\cos\left(\frac{A-B}{2}\right)}{\cos\left(\frac{A+B}{2}\right)} \times \tan\left(\frac{C}{2}\right)\) is a trigonometric identity that relates the tangent of half the sum of two angles to the cosine of half their difference, cosine of half their sum, and tangent of half the third angle in a triangle.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

Where:

• \(\cos\left(\frac{A-B}{2}\right)\) — Cosine of half the difference of angles A and B
• \(\cos\left(\frac{A+B}{2}\right)\) — Cosine of half the sum of angles A and B
• \(\tan\left(\frac{C}{2}\right)\) — Tangent of half of angle C

Explanation: This formula is derived from trigonometric identities and is particularly useful in triangle calculations where A + B + C = 180°.

3. Trigonometric Identities

Details: This identity is part of a family of trigonometric formulas that express relationships between different trigonometric functions and angles in a triangle.

4. Using the Calculator

Tips: Enter values for Cos (A-B)/2, Cos (A+B)/2, and Tan (C/2). Ensure Cos (A+B)/2 is not zero to avoid division by zero errors.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between A, B and C in this formula?
A: In a triangle, A + B + C = 180°, so C = 180° - (A + B).

Q2: Can this formula be used for any values of A and B?
A: The formula is valid for all angles where the trigonometric functions are defined and Cos (A+B)/2 ≠ 0.

Q3: What are the typical applications of this formula?
A: This formula is used in trigonometry problems, triangle solutions, and various engineering applications.

Q4: Are there any restrictions on the input values?
A: Cos (A+B)/2 cannot be zero, and all input values should be valid real numbers.

Q5: How precise are the calculations?
A: The calculator provides results with 6 decimal places precision, suitable for most applications.