Write sin(4t) - sin(2t) as a product.

1. Use sin a - sin b = 2 sin((a - b)/2) cos((a + b)/2) with a = 4t and b = 2t. 2. The half difference is (4t - 2t)/2 = 2t/2 = t. 3. The half sum is (4t + 2t)/2 = 6t/2 = 3t. 4. So the expression becomes 2 sin(t) cos(3t). 5. The option 2 sin(3t) cos(t) swaps the two half angles and would instead equal sin(4t) + sin(2t). 6. The option built from two cosines cannot vanish at t = 0, whereas the original expression does. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.4 Sum-to-Product and Product-to-Sum Formulas_