要证明这个表达式，我们可以尝试将其化简。首先，将分子和分母分别展开： 分子：sin(a) - cos(b) 分母：sin(b) - cos(a) 然后，将分子和分母分别展开： (sin(a) - cos(b))/(sin(b) - cos(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (sin(b)/sin(b) - cos(a)/sin(b)) 继续化简： = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cos(a)/sin(b)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (sin(b)/sin(b) - cos(a)/sin(b)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cos(a)/sin(b)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a) - cos(b))/sin(b) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a)/sin(b) - cos(b)/sin(b)) / (1 - cot(a)) = (sin(a