Sum/Difference Formulas

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

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

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

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

$$\text{sin}(150^\text{o}) = \frac{1}{2}$$ .

$$\text{cos}(75^\text{o}) = \frac{\text{√6} - \text{√2}}{4}$$ .

$$\text{cos}(175^\text{o} - 55^\text{o}) = \text{cos}(120^\text{o})$$ .

$$\text{cos}\frac{11\text{π}}{12} = \frac{-\text{√6} - \text{√2}}{4}$$ .

$$\frac{1}{2}$$ .

For complementary angles, $$\text{sin}(A) = \text{cos}(90^\text{o} - A)$$ .