Evaluate the following limit : lim(x→0) (cosec x - cot x)/x

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{cosec\,\text x - cot\,\text x}{\text x} \)

lim(x→0) (cosec x - cot x)/x

Answer 1

\(\lim\limits_{\text x \to0}\cfrac{cosec\,\text x - cot\,\text x}{\text x} \)

lim(x→0) (cosec x - cot x)/x

 To Find: Limits

NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form.

 In this Case, indeterminate Form is \(\infty \times\infty\)

cosec x - cot x = (1 - cos x)/sin x