Evaluate the given limit: \( \lim\limits_{x \to 0}(cosecx-cotx)\)

Asked by Abhisek | 1 year ago |  57

1 Answer

Solution :-

At x = 0, the value of the given function takes the form ∞−∞

Now, \( \lim\limits_{x \to 0}(cosecx-cotx)\)

\( \lim\limits_{x \to 0}(\dfrac{1}{sinx}-\dfrac{cosx}{sinx})\)

\( \lim\limits_{x \to 0}(\dfrac{1-cosx}{sinx})\)

\( \lim\limits_{x \to 0}(\dfrac{(\dfrac{1-cosx}{x})}{(\dfrac{sinx}{x})}\)

\( \dfrac{\lim\limits_{x \to 0}(\dfrac{1-cosx}{x})}{ \lim\limits_{x \to 0}(\dfrac{sinx}{x})}\)

\( \dfrac{0}{1}=0\)

Answered by Pragya Singh | 1 year ago

Related Questions