Expansion of cos (A + B + C)
We will learn how to find the expansion of cos (A + B + C). By using the formula of cos (α + β) and sin (α + β) we can easily expand cos (A + B + C).
Let us recall the formula of cos (α + β) = cos α cos β - sin α sin β and sin (α + β) = sin α cos β + cos α sin β.
cos (A + B + C) = cos [(A + B) + C]
= cos (A + B) cos C - sin (A + B) sin C, [applying the formula of cos (α + β)]
= (cos A cos B - sin A sin B) cos C - (sin A cos B + cos A sin B) sin C, [applying the formula of cos (α + β) and sin (α + β)]
= cos A cos B cos C - sin A sin B sin C - sin C sin A cos B - sin B sin C cos A, [applying distributive property]
= cos A cos B cos C (1 - tan A tan B - tan C tan A - tan B tan C)
Therefore, the expansion of cos (A + B + C) = cos A cos B cos C (1 - tan A tan B - tan C tan A - tan B tan C)
- Proof of Compound Angle Formula sin (α + β)
- Proof of Compound Angle Formula sin (α - β)
- Proof of Compound Angle Formula cos (α + β)
- Proof of Compound Angle Formula cos (α - β)
- Proof of Compound Angle Formula sin 22 α - sin 22 β
- Proof of Compound Angle Formula cos 22 α - sin 22 β
- Proof of Tangent Formula tan (α + β)
- Proof of Tangent Formula tan (α - β)
- Proof of Cotangent Formula cot (α + β)
- Proof of Cotangent Formula cot (α - β)
- Expansion of sin (A + B + C)
- Expansion of sin (A - B + C)
- Expansion of cos (A + B + C)
- Expansion of tan (A + B + C)
- Compound Angle Formulae
- Problems using Compound Angle Formulae
- Problems on Compound Angles
11 and 12 Grade Math
From Expansion of cos (A + B + C) to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns
Dec 13, 24 08:43 AM
We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r… -
Patterns in Math | Missing Number | Counting Numbers | Worksheets
Dec 13, 24 12:31 AM
Finding patterns in math is very important to understand the sequence in the series. We need to find the exact missing number that from the group of numbers. The counting numbers may be counting -
Concept of Pattern | Similar Patterns in Mathematics | Similar Pattern
Dec 12, 24 11:22 PM
Concept of pattern will help us to learn the basic number patterns and table patterns. Animals such as all cows, all lions, all dogs and all other animals have dissimilar features. All mangoes have si… -
2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line
Dec 12, 24 10:31 PM
2nd grade geometry worksheet -
Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical
Dec 09, 24 10:39 PM
What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.