Sum and Difference Formulae Table
In the previous section, we derived the formulas of all the sum and difference identities of the trigonometric functions sine, cosine, and tangent. Now, let us summarize these formulas in the table below for a quick revision.
Sum Formulae | Difference Formulae | |
---|---|---|
Sine function | sin (α + β) = sin α cos β + cos α sin β | sin (α – β) = sin α cos β – cos α sin β |
Cosine function | cos (α + β) = cos α cos β – sin α sin β | cos (α – β) = cos α cos β + sin α sin β |
Tangent function | tan (α + β) = (tan α + tan β)/(1 – tan α tan β) | tan (α – β) = (tan α – tan β)/(1 + tan α tan β) |
Sum and Difference Formulas
Sum and Difference formulas of trigonometry are used to calculate the values of trigonometric functions at any angle where it is feasible to express the given angle as the sum or the difference of standard angles like 0°, 30°, 45°, 60°, 90°, and 180°. For example, to evaluate the value of the cosine function at 15°, we can write 15° as the difference between 45° and 30°; i.e., cos 15° = cos (45°-15°). Now with the help of sum and difference formulae, we can easily solve the above problem. In this article, we will learn about various Sum and Difference formulae used in trigonometry in detail.
Table of Content
- Trigonometry Functions
- What are Sum and Difference Formulas?
- Sum and Difference Formulae
- Proof of Sum and Difference Identities
- Sum and Difference Formulas for Cosine
- Cos (α – β) formula
- Cos (α + β) formula
- Sum and Difference Formulas for Sine
- Sin (α – β) formula
- Sin (α + β) formula
- Sum and Difference Formulas for Tangent
- Tan (α – β) formula
- Tan (α + β) formula
- Sum and Difference Formulae Table
- How to Apply Sum and Difference Formulas
- Solved Examples on Sum and Difference Formulas