## 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

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