How to Apply Sin A + Sin B Formula?
Sin A + Sin B formula is used to solve various trigonometric problems, to apply the formula we can use the following steps:
Step 1: Determine the values of A and B in the expression sin A + sin B.
Step 2: Find the average (A + B)/2 and the difference (A – B)/2.
Step 3: Substitute the values in formula.
Step 4: Simplify
Let’s consider an example for the same.
Example: Simplify Sin 60° + Sin 30°.
Solution:
For Sin 60° + Sin 30°
A = 60° and B = 30°
- (A + B)/2 = (60 + 30)/2 = 45°, and
- (A – B)/2 = (60 – 30)/2 = 15°, and
Sin 60° + Sin 30° = 2 sin {60° + 30°}/2.cos {60° – 30°}/2
= 2 sin 45°.cos 15°
= 2 (1/√2) ((√3 + 1)/2√2)
= (√3 + 1)/2
Thus, Sin 60° + Sin 30° = (√3/2 + 1/2) = (√3 + 1)/2
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
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