Prosthaphaeresis

Prosthaphaeresis was an algorithm used in the late 16th century and early 17th century for approximating products using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally-applicable way of approximating products quickly. Its name comes from the Greek prosthesi and afairo, meaning addition and subtraction, two steps in the process.

Reverse identities

The product formulas can also be manipulated to obtain formulas that express addition in terms of multiplication. Although less useful for computing products, these are still useful for deriving trigonometric results:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• sin a + sin b = 2sincos
• sin a - sin b = 2cossin
• cos a + cos b = 2coscos
• cos a - cos b = -2sinsin