Question

Value of limx → 0⁡(1+cot(x))sin(x)
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Answer 1

Step-by-step explanation:

SOLUTION

TO EVALUATE

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

x→0

lim

(1+cotx)sinx

EVALUATION

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

x→0

lim

(1+cotx)sinx

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

x→0

lim

(1+

sinx

cosx

)sinx

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

x→0

lim

(

sinx

sinx+cosx

)sinx

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

x→0

lim

(sinx+cosx)

= ( {\sin 0 + \cos 0})=(sin0+cos0)

= 0 + 1=0+1

= 1=1

Answer 2

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