Limit with trigonometric functions

[Jules18]

Homework Statement

True or false?

lim Tanx/(1-Cosx) = lim Sec²x/Sinx = Infinity

(limits are as x approaches $$\pi$$ from the left)

The Attempt at a Solution

I tried just plugging $$\pi$$ into x in the first limit, and I ended up getting 0/2, which exists but is just 0. So I said false. Am I simplifying it too much? because what I did seems to make sense but it looks like that's not what they wanted me to do.

 

[mlarson9000]

Isn't it just 0/2=0?

 

[Mark44]

The original limit was neither of the indeterminate forms [0/0] or [infinity/infinity], so L'Hopital's Rule doesn't apply here. Your first approach was correct.