1. What is Product To Sum Identity?

The product-to-sum identities are trigonometric identities that convert products of trigonometric functions into sums or differences. They are useful for simplifying trigonometric expressions and solving integrals.

2. How Does the Calculator Work?

The calculator uses the product-to-sum identity:

Where:

• \( A \) — First angle in radians
• \( B \) — Second angle in radians
• \( \cos \) — Cosine function

Explanation: The identity shows that the product of two cosines can be expressed as the average of the cosines of the sum and difference of the angles.

3. Importance of Product To Sum Identities

Details: These identities are particularly useful in calculus for integrating products of trigonometric functions and in signal processing for analyzing waveforms.

4. Using the Calculator

Tips: Enter two angles in radians (π = 3.14159...). The calculator will show both the direct product and the equivalent sum form result.

5. Frequently Asked Questions (FAQ)

Q1: Are there other product-to-sum identities?
A: Yes, similar identities exist for sin A sin B and sin A cos B products.

Q2: Why use radians instead of degrees?
A: Radians are the standard unit in higher mathematics and calculus. Most programming languages' trigonometric functions use radians.

Q3: Can I use this for complex numbers?
A: The identity holds for complex arguments as well, though this calculator only handles real numbers.

Q4: What's the practical application of this identity?
A: It's used in Fourier analysis, solving differential equations, and simplifying trigonometric expressions.

Q5: How accurate are the calculations?
A: The calculations use PHP's built-in cos() function which has high precision, though results are rounded to 6 decimal places.