Limits of a Trigonometric Function

[dekoi]

Question:

lim(x->0) for (tanx - sinx) / (sinx)^2

This is what I got:

= (sinx-sinxcosx) / (cosx)(sinx)^2
= (sinx)(1-cosx) / (sinx)(sinx)(cosx)
= (1 - cosx) / (sinx)(cosx)

However, I can't figure out what to do from this step, as the limit still equals 0/0 at this stage.

 

[mezarashi]

Why are we posting twice -_-

 

[dekoi]

More people in this forum...

 

[lurflurf]

This is much like this one
https://www.physicsforums.com/showthread.php?t=90765&highlight=trig+friend
Many people must get problems of the sam bathroom wall.

 

[CarlB]

You might see if you can use this handy trig fact:

$$(1 + \cos(x))(1-\cos(x)) = 1-\cos^2(x) = \sin^2(x)$$

Carl