Sum to Product: sin A + sin B

This identity rewrites the sum of two sine values as a product involving the average angle and half the difference of the angles. It comes from the angle addition and subtraction formulas for sine: adding sin(A) and sin(B) and then regrouping the terms produces a factor of 2 sin((A+B)/2) and a cosine term that measures how far apart the angles are. It is especially useful because a messy sum can become easier to simplify, factor, or evaluate exactly.

Use this when you need to simplify expressions like sin(75°) + sin(15°), solve trigonometric equations, or transform sums into products for factoring. It is also useful in signal processing and wave analysis, where combining two oscillations into an amplitude-modulated product form is often easier to interpret.

• Using (A-B) instead of (A-B)/2 in the cosine factor
• Forgetting that the average angle is (A+B)/2, not (A+B)
• Swapping sine and cosine in the product form