Find the derivative of the functions: cosec x

Asked by Abhisek | 1 year ago |  50

##### Solution :-

$$f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}$$

$$\lim\limits_{h \to 0} \dfrac{1}{h}[cosec(x+h)-cosecx]$$

$$\lim\limits_{h \to 0} \dfrac{1}{h}[\dfrac{1}{sin(x+h)}-\dfrac{1}{sinx}]$$

$$\lim\limits_{h \to 0} \dfrac{1}{h}[\dfrac{sinx-sin(x+h)}{sinxsin(x+h)}]$$

$$- \dfrac{1}{sinx}\times 1\times \dfrac{cos(\dfrac{2x+0}{2})}{sin(x+0)}$$

$$- \dfrac{1}{sinx}\times \dfrac{cosx}{sinx}$$

= -cosecxcotx

Answered by Pragya Singh | 1 year ago

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