Evaluate the following limit : lim(x→0) (cot 2x - cosec 2x)/x

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{cot\,2\text x-cosec\,2\text x}{\text x} \)

lim(x→0) (cot 2x - cosec 2x)/x

Answer 1

\(\lim\limits_{\text x \to0}\cfrac{cot\,2\text x-cosec\,2\text x}{\text x} \)

lim(x→0) (cot 2x - cosec 2x)/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 2x - cot 2x = (1 - cos 2x)/sin 2x