Examples Using Sin A – Sin B
Example 1: Find the value of sin 145° – sin 35° using sin A + sin B identity.
Solution:
We know,
- Sin A – Sin B = 2 cos ½ (A + B) sin ½ (A – B)
Here, A = 145°, B = 35°
sin 145° – sin 35° = 2 cos ½ (145° + 35°) sin ½ (65° – 35°)
= 2 cos 90° sin 15°
= 0 [∵cos 90º = 0]
Example 2: Verify the given expression using expansion of Sin A – Sin B: sin 70° – cos 70° = √2 sin 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 cos ½ (A + B) sin ½ (A – B)
⇒ sin 70° – sin 20° = 2 cos ½ (70° + 20°) sin ½ (70° – 20°)
= 2 cos 45° sin 25°
= √2 sin 25°
= R.H.S.
Hence, verified.
Sin A minus Sin B
Sin A minus Sin B is an important trigonometric formula. Sin A – Sin B formula, for two angles A and B, is given as, Sin A – Sin B = 2 cos (A + B)/2 sin (A – B)/2. This formula is also called the difference to product formula for sine.
In this article, we will learn about, Sin A – Sin B identity, Sin A – Sin B Formula, Proof of Sin A – Sin B Formula, related examples and others in detail.
Table of Content
- Sin A – Sin B Identity
- Sin A – Sin B Formula
- Proof of Sin A – Sin B Formula
- How to Apply Sin A – Sin B?
- Examples Using Sin A – Sin B