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

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

Let $\alpha$ and $\beta$ be two angles of right triangles. The sine functions with the two angles are written as $\sin{\alpha}$ and $\sin{\beta}$ mathematically. The sum of the two sine functions is written mathematically in the following form.

$\sin{\alpha}+\sin{\beta}$

The sum of sine functions can be transformed into the product of the trigonometric functions as follows.

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

The sum to product transformation rule of sin functions is popular written in two forms.

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

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

In the same way, you can write the sum to product transformation formula of sine functions in terms of any two angles.

Learn how to prove the sum to product transformation identity of sine functions in trigonometry.

Latest Math Topics

Jun 05, 2023

Jun 01, 2023

May 21, 2023

May 16, 2023

May 10, 2023

Latest Math Problems

Jun 08, 2023

May 09, 2023

A best free mathematics education website that helps students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved