Question

Value of limx → 0⁡(1+Sin(x))Cosec(x)​

Answer 1

Step-by-step explanation:

We have,

$\lim _{x \rarr0 } (1 + \sin(x) ) \cosec(x)$

$= \lim_{x \rarr0 } \frac{1 + \sin(x) }{ \sin(x) }$

$= \lim_{x \rarr0 } \frac{ \frac{d}{dx}(1 + \sin(x) ) }{ \frac{d}{dx}( \sin(x) ) }$

$= \lim_{x \rarr0 } \frac{ \cos(x) }{ \cos(x) }$

$= \lim_{x \rarr0 } 1$

$= 1$