Stuck on this limit, with inverse tan/sin

[studentCal]

Stuck after some tries on this one ;




The solution shud be: -1

any ideas/tip?

 

[srmichael]

Have you tried L'Hospital's rule?

 

[studentCal]

yes, tried, but my answer becomes bigger and bigger, not even close to -1

 

[srmichael]

Yes, it does. But, as with some problems, you have to apply the rule more than once. In this case, three times. Then you should see the light at the end of the tunnel.

 

[galactus]

note that tan and sin behave like x near 0.

So, you essentially have \(\displaystyle \frac{1-x}{x-1}\)

Which equals what?.