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