# Expansion of sin (A - B + C)

We will learn how to find the expansion of sin (A - B + C). By using the formula of sin (A + B), sin (A - B) and cos (A - B) we can easily expand sin (A - B + C).

Let us recall the formula of sin (α + β) = sin α cos β + cos α sin β, sin (α - β) = sin α cos β - cos α sin β and cos (α - β) = cos α cos β + sin α sin β.

sin (A - B + C) = sin [( A - B) + C]

= sin (A - B) cos C + cos (A - B) sin C, [applying the formula of sin (α + β)]

= (sin A cos B - cos A sin B) cos C + (cos A cos B + sin A sin B) sin C, [applying the formula of sin (α - β) and cos (α - β)]

= sin A cos B cos C - sin B cos C cos A + sin C cos A cos B + sin A sin B sin C, [applying distributive property]

= sin A cos B cos C - cos A sin B cos C + cos A cos B sin C + sin A sin B sin C

Therefore, the expansion of sin (A - B + C) = sin A cos B cos C - cos A sin B cos C + cos A cos B sin C + sin A sin B sin C.

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.

 Share this page: What’s this?

## Recent Articles

1. ### Method of L.C.M. | Finding L.C.M. | Smallest Common Multiple | Common

Apr 15, 24 01:29 AM

We will discuss here about the method of l.c.m. (least common multiple). Let us consider the numbers 8, 12 and 16. Multiples of 8 are → 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ......

Read More

2. ### Common Multiples | How to Find Common Multiples of Two Numbers?

Apr 15, 24 01:13 AM

Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24…

Read More

3. ### Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

Apr 14, 24 03:06 PM

The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is t…

Read More

4. ### Worksheet on H.C.F. | Word Problems on H.C.F. | H.C.F. Worksheet | Ans

Apr 14, 24 02:23 PM

Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers…

Read More

5. ### Common Factors | Find the Common Factor | Worksheet | Answer

Apr 14, 24 02:01 PM

Common factors of two or more numbers are a number which divides each of the given numbers exactly. For examples 1. Find the common factor of 6 and 8. Factor of 6 = 1, 2, 3 and 6. Factor

Read More