1. The problem is to match the given trigonometric formulas/identities (A-L) with the numbered formulas 1 to 9. 2. We start by identifying each formula/identity letter with its corresponding expression: A. $\sin(x)\cos(y) - \cos(x)\sin(y)$ (Difference formula for sine) B. $\pm \sqrt{\frac{1-\cos(x)}{2}}$ (Half-angle identity for sine) C. $\frac{\tan(x) - \tan(y)}{1 + \tan(x)\tan(y)}$ (Difference formula for tangent) D. $\frac{2\tan(x)}{1 - \tan^2(x)}$ (Double angle formula for tangent) E. $\sin(x)\cos(y) + \cos(x)\sin(y)$ (Sum formula for sine) F. $\frac{1 - \cos(x)}{\sin(x)}$ (Tangent half-angle identity) G. $\frac{\tan(x) + \tan(y)}{1 - \tan(x)\tan(y)}$ (Sum formula for tangent) H. $1 - 2\sin^2(x)$ (Double angle formula for cosine) I. $\cos(x)\cos(y) + \sin(x)\sin(y)$ (Cosine difference formula) J. $2\sin(x)\cos(x)$ (Double angle formula for sine) K. $\cos^2 x + \sin^2 x = 1$ (Pythagorean identity) L. $\pm \sqrt{\frac{1+\cos(x)}{2}}$ (Half-angle identity for cosine) 3. Now match these with the numbered formulas: 1) $\sin(x - y)$ corresponds to A. 2) Pythagorean Identity corresponds to K. 3) $\sin(2x) = 2\sin(x)\cos(x)$ corresponds to J. 4) $\cos(2x)$ corresponds to H. 5) $\tan\left(\frac{x}{2}\right)$ corresponds to F. 6) $\tan(2x)$ corresponds to D. 7) $\sin(x + y)$ corresponds to E. 8) $\tan(x + y)$ corresponds to G. 9) $\cos(x - y)$ corresponds to I. Final answers: 1) A 2) K 3) J 4) H 5) F 6) D 7) E 8) G 9) I