Trig Identity Limit: Solving Trig Identities with Difficulty

[synergix]

Homework Statement

lim t³/tan³2t
t->0

The Attempt at a Solution

I am stuck I have a lot of trouble with trig identities

 

[Bohrok]

Do you know L'hôpital's rule? That might be the easiest way. If not, rewrite tan2t as sin2t/cos2t first. cos(2*0) won't cause a problem, but the t and sin2t will. See if you can get it to look like sin2t/t.

 

[synergix]

lim= 2*t*2*t*2*t*cos³2t/2*sin2t*2*sin2t*2*sin2t\


so all the 2*t cancel the sin2t leaving cos³2t/2*2*2 so limit=1/6

is this correct??

 

[Bohrok]

2*2*2=8, not 6.

 

[synergix]

haha you wow. :)