Final answer:
To prove the Double-Angle Formula for Sine using the Addition Formula for Sine, substitute 'a' with 'x' and 'B' with 'x' in the Addition Formula, then use the Double-Angle Formula.
Step-by-step explanation:
To prove the Double-Angle Formula for Sine using the Addition Formula for Sine, we start with the Addition Formula for Sine:
sin(a + B) = sin a * cos B + cos a * sin B
Next, we substitute 'a' with 'x' and 'B' with 'x' in the Addition Formula for Sine:
sin(x + x) = sin x * cos x + cos x * sin x
Using the Double-Angle Formula for Sine:
sin(2x) = 2sin x * cos x
Therefore, the Double-Angle Formula for Sine is proven using the Addition Formula for Sine.