1. What is Cos A + Cos B Formula?

The formula \(\cos A + \cos B = 2 \cdot \cos\left(\frac{A+B}{2}\right) \cdot \cos\left(\frac{A-B}{2}\right)\) is a fundamental trigonometric identity that expresses the sum of two cosine functions as a product of cosine functions.

2. How Does the Calculator Work?

The calculator uses the trigonometric identity:

Where:

• \( A \) — Angle A in radians
• \( B \) — Angle B in radians
• \( \cos \) — Cosine trigonometric function

Explanation: This identity transforms the sum of two cosine functions into a product, making it easier to simplify and solve trigonometric expressions.

3. Importance of Trigonometric Identities

Details: Trigonometric identities like this one are essential for simplifying complex trigonometric expressions, solving equations, and analyzing periodic phenomena in mathematics, physics, and engineering.

4. Using the Calculator

Tips: Enter angles A and B in radians. The calculator will compute the sum of their cosine values using the trigonometric identity formula.

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: This calculator requires input in radians. Convert degrees to radians by multiplying by π/180.

Q2: What is the range of valid inputs?
A: The cosine function accepts any real number, but angles are typically between -2π and 2π radians.

Q3: How accurate are the results?
A: Results are accurate to 6 decimal places, using PHP's built-in cosine function.

Q4: Can this formula be derived from other identities?
A: Yes, this identity can be derived from the sum-to-product formulas in trigonometry.

Q5: What are practical applications of this identity?
A: This identity is used in signal processing, wave analysis, and solving trigonometric equations in various scientific fields.