1 Answer
Solution :-
\( f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h} \)
\( \lim\limits_{h \to 0} \dfrac{1}{h}[cosec(x+h)-cosecx]\)
\( \lim\limits_{h \to 0} \dfrac{1}{h}[\dfrac{1}{sin(x+h)}-\dfrac{1}{sinx}]\)
\( \lim\limits_{h \to 0} \dfrac{1}{h}[\dfrac{sinx-sin(x+h)}{sinxsin(x+h)}]\)
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\(- \dfrac{1}{sinx}\times 1\times \dfrac{cos(\dfrac{2x+0}{2})}{sin(x+0)}\)
\(- \dfrac{1}{sinx}\times \dfrac{cosx}{sinx}\)
= -cosecxcotx
Answered by Pragya Singh | 1 year ago