Tan A - Tan B Calculator

Formula Used:

\[ \tan A - \tan B = \frac{\sin(A-B)}{\cos A \cdot \cos B} \]

Tan A - Tan B:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Tan A - Tan B Formula?

The formula \(\tan A - \tan B = \frac{\sin(A-B)}{\cos A \cdot \cos B}\) is a trigonometric identity that expresses the difference of two tangent functions in terms of sine and cosine functions. This identity is useful for simplifying trigonometric expressions and solving equations.

2. How Does the Calculator Work?

The calculator uses the trigonometric identity:

\[ \tan A - \tan B = \frac{\sin(A-B)}{\cos A \cdot \cos B} \]

Where:

\( A \) — First angle in degrees
\( B \) — Second angle in degrees
\( \sin(A-B) \) — Sine of the difference between angles A and B
\( \cos A \) — Cosine of angle A
\( \cos B \) — Cosine of angle B

Explanation: The calculator converts angles from degrees to radians, computes the sine and cosine values, then applies the formula to calculate the result.

3. Importance of Trigonometric Identities

Details: Trigonometric identities like this one are fundamental in mathematics, physics, and engineering. They help simplify complex expressions, solve equations, and prove other mathematical theorems.

4. Using the Calculator

Tips: Enter angles A and B in degrees. The calculator will compute the result using the trigonometric identity. Note that the result is undefined when either cos A or cos B equals zero.

5. Frequently Asked Questions (FAQ)

Q1: When is the result undefined?
A: The result is undefined when either cos A or cos B equals zero, which occurs when A or B is 90° + k·180° (where k is an integer).

Q2: Can I use this calculator for angles in radians?
A: This calculator expects angles in degrees. For radians, you would need to convert them to degrees first or modify the calculator.

Q3: What are some practical applications of this identity?
A: This identity is used in signal processing, wave analysis, and solving trigonometric equations in various engineering and physics problems.

Q4: How accurate are the calculations?
A: The calculations use PHP's built-in trigonometric functions, which provide high precision for most practical purposes.

Q5: Can this identity be derived from basic trigonometric formulas?
A: Yes, this identity can be derived using the sine and cosine addition formulas and the definition of tangent as sine divided by cosine.