How to Apply Sum and Difference Formulas
Sum and Difference Formulas of trigonometry are used to solve various trigonometry problems and find the values of trigonometric functions without standard values. To Apply Sum and Difference Formulas study the following example,
Example: Find the value of sin 15°
Solution:
Step 1: Write the given function in the sum and difference of the standard function,
sin 15° = sin (45 -30)°
Step 2: Use the required Sum and Difference Formulas, here we use, sin (α – β) = sin α cos β – cos α sin β
sin (45 -30)° = sin 45° cos 30° – cos 45° sin 30°
Step 3: Substitute the value of these standard trigonometric functions using the trigonometric table.
sin (45 -30)° = 1/√2 × √3/2 – 1/√2 × 1/2
Step 4: Simplify the value obtained in the above step.
sin (45 -30)° = 1/√2 × √3/2 – 1/√2 × 1/2
= (√3 -1)/ 2√2
sin 15° = (√3 -1)√2 / 4
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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