\(\lim_{x\rightarrow 0}(cosec\,x-cot\,x)\) At x = 0, the value of the given function takes the form ∞ to -∞. Now, =\(\lim_{x\rightarrow 0}(cosec\,x-cot\,x)\) = \(\lim_{x\rightarrow 0}(\frac{1}{x}-\frac{cos\,x}{sin\,x})\) = \(\lim_{x\rightarrow 0}({1}-\frac{cos\,x}{sin\,x})\) = \(\lim_{x\rightarrow 0}\)\(\frac{1-\frac{cis\,x}{x}}{\frac{x}{\frac{son\,x}{x}}}\) =\(\frac{\lim_{x\rightarrow 0}1-\frac{cos\,x}{x}}{\lim_{x\rightarrow 0}\frac{sin\,x}{x}}\) = \(\frac{0}{1}\) [= \(\lim_{x\rightarrow 0}\) ( \(1-\frac{cos\,x}{x}\)) = 0 and \(\lim_{x\rightarrow 0}\)\(\frac{sin\,x}{x}\) = 1] =0