I Think in a triangle, A + B + C = 180 degrees. Therefore, A = 180 - (B + C). Subtituting in the equation Sin A = Sin B Cos C + Sin C cos B, we get Sin [180 - (B + C)] = Sin B Cos C + Sin C cos B. Since in the Second Quadrant, Sine is positive and Sine remains Sine, Sin (B + C) = Sin B Cos C + Sin C cos B. Hence proved. I do not know how to express mathematically. Hope it is right. Good Souls comment on this.