A trigonometric identity that expresses the transformation of sum or difference of trigonometric functions into product form is called the sum or difference to product trigonometric identities.

In mathematics, the trigonometric functions are involved in fundamental operations like addition or subtraction. If the angles in the trigonometric functions are same, we know how to add or subtract them directly but we cannot add or subtraction them directly if the angles in the trigonometric functions are different.

Hence, we should use the following transformation trigonometric identities to add or subtract trigonometric functions in mathematics.

$(1).\,\,\,$ $\sin{\alpha}+\sin{\beta}$ $\,=\,$ $2\sin{\Bigg(\dfrac{\alpha+\beta}{2}\Bigg)}\cos{\Bigg(\dfrac{\alpha-\beta}{2}\Bigg)}$

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

$(1).\,\,\,$ $\sin{\alpha}-\sin{\beta}$ $\,=\,$ $2\cos{\Bigg(\dfrac{\alpha+\beta}{2}\Bigg)}\sin{\Bigg(\dfrac{\alpha-\beta}{2}\Bigg)}$

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

Latest Math Topics

Dec 13, 2023

Jul 20, 2023

Jun 26, 2023

Latest Math Problems

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved