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

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

When the $\alpha$ and $\beta$ represent the two angles of right triangles, the sine functions with both angles are written as $\sin{\alpha}$ and $\sin{\beta}$ in mathematical form. The difference of the two sine functions is written in the following mathematical form in trigonometry.

$\sin{\alpha}-\sin{\beta}$

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

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

The difference to product transformation formula for the sin functions is written in two popular forms.

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

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

Thus, we can write the difference to product transformation formula for sine functions in terms of any two angles.

Learn how to derive the difference to product transformation identity of sine functions in mathematics.

Latest Math Topics

Mar 21, 2023

Feb 25, 2023

Feb 17, 2023

Feb 10, 2023

Latest Math Problems

Mar 03, 2023

Mar 01, 2023

Feb 27, 2023

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

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

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved