Sum and Difference Identities

The Sum Identity for Cosine states that $$\text{cos}(A + B) = \text{cos}(A)\text{cos}(B) - \text{sin}(A)\text{sin}(B)$$ .

The Difference Identity for Cosine states that $$\text{cos}(A - B) = \text{cos}(A)\text{cos}(B) + \text{sin}(A)\text{sin}(B)$$ .

The Sum Identity for Sine states that $$\text{sin}(A + B) = \text{sin}(A)\text{cos}(B) + \text{cos}(A)\text{sin}(B)$$ .

The Difference Identity for Sine states that $$\text{sin}(A - B) = \text{sin}(A)\text{cos}(B) - \text{cos}(A)\text{sin}(B)$$ .

The formula for Tangent of a Sum is $$\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$$ .

The formula for Tangent of a Difference is $$\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$$ .

The exact value is $$\frac{1}{2}$$ .

$$\text{cos}(A + B) = \text{cos}(A)\text{cos}(B) - \text{sin}(A)\text{sin}(B)$$ .

It can be written as $$\text{cos}(120)$$ .

$$\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$$ .