Compound Angles Sum AndDifferences





In this page compound angles sum anddifferences we are going to see combination of two formulas in compound angles.

We already know these two formulas

Sin (A+B) = Sin A cos B + Cos A sin B -----(1)

Sin (A-B) = Sin A cos B - Cos A sin B -----(2)

by adding (1) + (2) we will get the new formula

Sin(A+B)+Sin (A-B)=Sin A cos B+Cos A sin B+Sin A cos B-Cos A sin B

                          = 2 Sin A cos B

The new formula is Sin(A+B)+Sin (A-B) = 2 Sin A cos B

by subtracting (1) - (2) we will get the new formula

Sin(A+B)-Sin (A-B)=Sin A cos B+Cos A sin B-[Sin A cos B-Cos A sin B]

Sin(A+B)-Sin (A-B)=Sin A cos B+Cos A sin B-Sin A cos B+Cos A sin B

                         = Cos A sin B + Cos A sin B

                          = 2 Cos A sin B

So the new formula is Sin(A+B)-Sin (A-B) = 2 Cos A sin B

Cos (A+B) = Cos A cos B - sin A sin B -----(1)

Cos (A-B) = Cos A cos B + sin A sin B -----(2)

by adding (1) + (2) we will get the new formula

Cos(A+B)+Cos (A-B) = Cos A cos B-sin A sin B+Cos A cos B+sin A sin B

                            = 2 Cos A cos B

So the new formula is Cos(A+B)+Cos (A-B) = 2 Cos A cos B

by subtracting (1) - (2) we will get the new formula

Cos(A+B)-Cos (A-B) = Cos A cos B-sin A sin B-[Cos A cos B+sin A sin B]

                            = Cos A cos B-sin A sin B-Cos A cos B-sin A sin B

                            = -2sin A sin B

So the new formula is Cos(A+B)-Cos (A-B) = -2sin A sin B

The new derived formulas are  Compound Angles Sum AndDifferences

1.Sin(A+B)+Sin (A-B) = 2 Sin A cos B

2.Sin(A+B)-Sin (A-B) = 2 Cos A sin B

3.Cos(A+B)+Cos (A-B) = 2 Cos A cos B

4.Cos(A+B)-Cos (A-B) = -2sin A sin B

Related Topics

  1. Trigonometric Ratios
  2. Trigonometric Identities
  3. Complementary Angles
  4. Values Of Certain Angles
  5. Heights And Distances
  6. Double Angle Formulas
  7. Half Angle Formulas
  8. Compound Angle Formulas
  9. 3A formulas
  10. Sum to product forms
  11. Trigonometry-Problems Using Identities
  12. Trigonometry Practical Problems

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”Compound Angles Sum AndDifferences

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