Question

Value of limx → 0⁡(1+cot(x))sin(x)​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \lim_{x \to 0} \: (1 + \cot x) \sin x$

EVALUATION

$\displaystyle \lim_{x \to 0} \: (1 + \cot x) \sin x$

$= \displaystyle \lim_{x \to 0} \: \bigg(1 + \frac{ \cos x}{ \sin x} \bigg) \sin x$

$= \displaystyle \lim_{x \to 0} \: \bigg( \frac{\sin x + \cos x}{ \sin x} \bigg) \sin x$

$= \displaystyle \lim_{x \to 0} \: ( {\sin x + \cos x})$

$= ( {\sin 0 + \cos 0})$

$= 0 + 1$

$= 1$

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Answer 2

Step-by-step explanation:

write the answer explain plz