Sum to Product Formulas
Sum-to-product formulas in trigonometry convert the sum of sine and cosine functions to product form. They help to easily solve the sum problems the sum-to-product formulas are,
Formula of sin A plus sin B, i.e. (sin A + sin B)
sin A + sin B = 2 sin [(A+B)/2] × cos [(A-B)/2]
Formula of sin A minus sin B, i.e. (sin A – sin B)
sin A – sin B = 2 cos[(A+B)/2] × sin[(A-B)/2]
Formula of cos A plus cos B, i.e. (cos A + cos B)
cos A + cos B = 2 cos[(A+B)/2] × cos[(A-B)/2]
Formula of cos A minus cos B, i.e. (cos A – cos B)
cos A – cos B = 2 sin[(A+B)/2] × sin[(A-B)/2]
Sum to Product Formulas
The sum to product formulas are trigonometric identities that convert the sum or difference of two trigonometric functions into a product of trigonometric functions. These formulas are particularly useful in simplifying expressions, solving trigonometric equations, and integrating functions.
Sum to Product formulas are important formulas of trigonometry. Four sum-to-product formulas in trigonometry are,
- sin A + sin B = 2 sin [(A+B)/2] × cos [(A-B)/2]
- sin A – sin B = 2 cos[(A+B)/2] × sin[(A-B)/2]
- cos A + cos B = 2 cos[(A+B)/2] × cos[(A-B)/2]
- cos A – cos B = 2 sin[(A+B)/2] × sin[(A-B)/2]
In this article, we will learn about Sum to Product Formulas, Proof of Sum to Product Formulas, Application of Sum to Product Formulas in detail.