Limit and Trigonometry

[getoutofmylaboratory]

Assume that lim sin(x)/x = 1 as x approaches 0.

lim x^2 csc^2 x
x -> 0

I know that csc = 1/sin. I found a post for this same problem that explain the steps like so:

x^2/sin^2(x) =[ x/sin(x)] * [ x/sin(x)].

Since limit ( x->0) x/sin(x) = 1 then the limit is equal to 1*1 = 1

Would someone please explain this to me? I understand that csc^2 would equal 1/sin * 1/sin, but where is the x/sin(x) coming from?

 

[Deleted member 4993]

Assume that lim sin(x)/x = 1 as x approaches 0.

lim x^2 csc^2 x
x -> 0

I know that csc = 1/sin. I found a post for this same problem that explain the steps like so:



Would someone please explain this to me? I understand that csc^2 would equal 1/sin * 1/sin, but where is the x/sin(x) coming from?

\(\displaystyle \displaystyle {x^2 * csc^2(x) \ = \ \frac{x^2}{sin^2(x)} \ = \ \frac{x \ * \ x}{sin(x) \ * \ sin(x)} \ =\ \frac {x}{sin(x)} \ * \ \frac {x}{sin(x)}}\)

 

[getoutofmylaboratory]

Thanks. I was looking more for an explanation on it, but ended up getting it elsewhere.

 

[stapel]

Thanks. I was looking more for an explanation on it, but ended up getting it elsewhere.

For reference' sake and for the sake of future students, kindly please post the help you received which clarified how the x^2 worked in the exercise. Thank you!