Maths Question ~ Mathematicians please help!

[titaniumx3]

I would really appreciate some advice concerning this question.

QUESTION:

Show that for any real number n.

limit as x->0 of sin(n*x)/sin(x) = n

Now I'm pretty sure you have to use a well known limit such as the one for sin(x)/x but I'm confused as to how you get it into that form. I fear I'm just missing a very obvious trig identity here.

Any ideas?

 

[titaniumx3]

Its degree level and part of real and complex variable theory. They're basic questions revolving around theorems of the limits of functions. Its just that this one has me stumped!

 

[titaniumx3]

LOL, I just about remember doing L'Hôpital's rule last year but yeah I think thats probably the intended way. As for small angle approximations, that would make sense too since I'm not really being asked to prove anything. I just expecting some sort of subtitution/rearrangement job tbh.

Thanks again!


EDIT: I just realised that you can actually rearrange the formula to give:

sin(nx)/nx * n * 1/(sin(x)/x)

Hence as x->0, you're left with n.