Product-to-Sum Identities

1 . \sin α \cdot \sin β = \frac{1}{2} [\cos (α - β) - \cos (α + β)]

2 . \cos α \cdot \cos β = \frac{1}{2} [\cos (α - β) + \cos (α + β)]

3 . \sin α \cdot \cos β = \frac{1}{2} [\sin (α + β) + \sin (α - β)]

4 . \cos α \cdot \sin β = \frac{1}{2} [\sin (α + β) - \sin (α - β)]

5 . \tan α \cdot \tan β = \frac{(\tan α + \tan β)}{(\cot α + \cot β)}

6 . \cot α \cdot \cot β = \frac{(\cot α + \cot β)}{(\tan α + \tan β)}

7 . \tan α \cdot \cot β = \frac{(\tan α + \cot β)}{(\cot α + \tan β)}

\cos α \cdot \cos β = \frac{1}{2} [\cos (α - β) + \cos (α + β)]

\cos 3 x \cdot \cos 2 x = \frac{1}{2} [\cos (3 x - 2 x) + \cos (3 x + 2 x)]

\cos 3 x \cdot \cos 2 x = \frac{1}{2} [\cos x + \cos 5 x]

\cos 3 x \cdot \cos 2 x = \frac{\cos x}{2} + \frac{\cos 5 x}{2}