Summary on Sum to Product Formula
- Sum to product formulas is used to find expression for sum and difference of sines and cosines functions as products of sine and cosine functions.
- 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 sin [(A – B)/2] cos [(A + B)/2]
- cos A – cos B = -2 sin [(A + B)/2] sin [(A – B)/2]
- cos A + cos B = 2 cos [(A + B)/2] cos [(A – B)/2]
- To derive sum to product formula we use product to sum formulas in trigonometry.
- These formulas helps to simplify trigonometric problems.
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.
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