Sum-to-Product Identities

1. Sine Sum and Difference

• Sum of Sines:

  $$\sin A+\sin B=2\sin \left(\frac{A+B}{2}\right)\cos \left(\frac{A-B}{2}\right)$$

• Difference of Sines:

  $$\sin A-\sin B=2\cos \left(\frac{A+B}{2}\right)\sin \left(\frac{A-B}{2}\right)$$

2. Cosine Sum and Difference

• Sum of Cosines:

  $$\cos A+\cos B=2\cos \left(\frac{A+B}{2}\right)\cos \left(\frac{A-B}{2}\right)$$

• Difference of Cosines:

  $$\cos A-\cos B=-2\sin \left(\frac{A+B}{2}\right)\sin \left(\frac{A-B}{2}\right)$$