1. What is the Tan A in Terms of Tan A/2 Formula?

The formula \(\tan A = \frac{2 \cdot \tan(A/2)}{1 - \tan^2(A/2)}\) is a trigonometric identity that expresses the tangent of an angle A in terms of the tangent of half that angle. This is derived from the double-angle formula for tangent.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \tan A \) — Tangent of angle A
• \( \tan(A/2) \) — Tangent of half angle A/2

Explanation: This formula allows calculation of the tangent of a full angle when only the tangent of half that angle is known.

3. Importance of the Formula

Details: This trigonometric identity is particularly useful in solving trigonometric equations, simplifying expressions, and in various applications of trigonometry including physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter the value of tan(A/2) in the input field. The calculator will compute and display the value of tan A based on the provided input.

5. Frequently Asked Questions (FAQ)

Q1: What are the domain restrictions for this formula?
A: The formula is undefined when \( \tan^2(A/2) = 1 \), which occurs when A/2 = 45° + k·90° (where k is an integer).

Q2: Can this formula be used for any angle A?
A: Yes, the formula works for all angles except those where the denominator becomes zero.

Q3: How is this formula derived?
A: The formula is derived from the double-angle formula for tangent: \( \tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta} \), where θ = A/2.

Q4: What are practical applications of this formula?
A: This formula is used in trigonometric calculations, solving equations, and in various fields including navigation, physics, and engineering.

Q5: Can negative values be used for tan(A/2)?
A: Yes, the formula works for both positive and negative values of tan(A/2), as long as the denominator doesn't become zero.