Solved Examples on Sin A + Sin B Formula
Example 1: Find the value of sin 145° + sin 35° using sin A + sin B identity.
Solution:
We know, Sin A + Sin B = 2 sin½ (A + B) cos ½ (A – B)
Here, A = 145°, B = 35°
sin 145° + sin 35° = 2 sin½ (145° + 35°) cos ½ (65° – 35°)
⇒ sin 145° + sin 35° = 2 sin 90° cos 15°
⇒ sin 145° + sin 35° = 2 x 1 x ((√3 + 1)/2√2)
⇒ sin 145° + sin 35° =((√3 + 1)/√2)
Example 2: Verify the given expression using expansion of Sin A + Sin B: sin 70° + cos 70° = √2 cos 25°
Solution:
L.H.S. = sin 70° + cos 70°
Since, cos 70° = cos(90° – 20°) = sin 20°
sin 70° + cos 70° = sin 70° + sin 20°
Using Sin A + Sin B = 2 sin½ (A + B) cos ½ (A – B)
L.H.S. = sin 70° + sin 20° = 2 sin½ (70° + 20°) cos ½ (70° – 20°)
⇒ L.H.S. = 2 sin 45° cos 25°
⇒ L.H.S. = 2.(1/√2).cos 25° = √2 cos 25°
⇒ L.H.S. = R.H.S.
Hence, verified.
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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