$\cos{\alpha}+\cos{\beta}$ $\,=\,$ $2\cos{\Big(\dfrac{\alpha+\beta}{2}\Big)}\cos{\Big(\dfrac{\alpha-\beta}{2}\Big)}$

An identity that expresses the transformation of sum of cosine functions into product form is called the sum to product identity of cosine functions.

When $\alpha$ and $\beta$ represent two angles of the right triangles. The cosine of the two angles are written as $\cos{\alpha}$ and $\cos{\beta}$ in trigonometric mathematics. The sum of the two cosine functions is written mathematically as follows.

$\cos{\alpha}+\cos{\beta}$

The sum of cosine functions can be transformed into the product of the trigonometric functions in the following mathematical form.

$\implies$ $\cos{\alpha}+\cos{\beta}$ $\,=\,$ $2\cos{\Big(\dfrac{\alpha+\beta}{2}\Big)}\cos{\Big(\dfrac{\alpha-\beta}{2}\Big)}$

The sum to product transformation rule of cosine functions is also popularly written in the following two forms in mathematics.

$(1). \,\,\,$ $\cos{x}+\cos{y}$ $\,=\,$ $2\cos{\Big(\dfrac{x+y}{2}\Big)}\cos{\Big(\dfrac{x-y}{2}\Big)}$

$(2). \,\,\,$ $\cos{C}+\cos{D}$ $\,=\,$ $2\cos{\Big(\dfrac{C+D}{2}\Big)}\cos{\Big(\dfrac{C-D}{2}\Big)}$

Thus, you can write the sum to product transformation formula for cosine functions in terms of any two angles.

Learn how to derive the sum to product transformation identity of cosine functions in trigonometry.

Latest Math Topics

Jul 20, 2023

Jun 26, 2023

Jun 23, 2023

Latest Math Problems

Jul 01, 2023

Jun 25, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved