Final answer:
The identity sin(α-β) = sinαcosβ - cosαsinβ can be proved using the sine sum and difference formulas, specifically the difference case, demonstrating the correctness of this trigonometric identity.
Step-by-step explanation:
The equation sin(α-β)=sinαcosβ-sinβcosα is a trigonometric identity that can be proved using the sum and difference formulas for sine.
Proof of Sin(α-β)
Start with the sum and difference formulas:
sin(α±β) = sinαcosβ ± cosαsinβ
For the subtraction case (α-β), the formula becomes:
sin(α-β) = sinαcosβ - cosαsinβ
This is the identity we set out to prove, and it is now evident that it holds true based on the established sum and difference formulas for sine.