Sin A + Sin B Formula Proof
Proof of Sin A + Sin B can be explained very easily using the expansion of simple trigonometric identities that is sin(A + B) and sin(A – B) formula:
- sin(A + B) = sin A cos B + cos A sin B . . . (i)
- sin(A – B) = sin A cos B – cos A sin B . . . (ii)
Adding equation (i) and (ii)
sin(A + B) + sin(A – B) = 2 sin A cos B . . . (iii)
Assume angles X and Y, such that X = A + B and Y = A – B.
Solving X = A + B and Y = A – B , we found
A = (X + Y)/2 and B = (X – Y)/2
Replace A and B in eq (iii)
⇒ sin X + sin Y = 2sin{(X + Y)/2} .cos {(X – Y)/2}
or we can say Sin A + Sin B = 2 {sin(A + B)/2 }.cos {(A – B)/2}
Hence proved.
Sin A + Sin B Formula
Sin A + Sin B Formula is a very significant formula in trigonometry, enabling the calculation of the sum of sine values for angles A and B. Sin A + Sin B Formula provides a way to express the sum of two sine functions in terms of the product of sine and cosine functions. It is given as:
Sin A + Sin B = 2 {sin(A + B)/2 }.cos {(A – B)/2}
This formula is used in various problems in both theoretical and practical trigonometry. It is also referred to as the Sum to Product Formula for sine. In this article, we will discuss the formula, its derivation, and some solved examples as well.
Table of Content
- Trigonometry Identities
- Sin A + Sin B Formula
- Sin A + Sin B Formula Proof
- How to Apply Sin A + Sin B Formula?
- Sin A + Sin B + Sin C Formula
- Solved Examples on Sin A + Sin B Formula
- Practice Problems on Sin A + Sin B Formula