trig limit: (sinx - tanx)/((sinx)^3) as x goes to 0

[rragas]

Hi. I'm having problems with dealing with trig limits in general. Here is an example of what I don't get.

lim x=>0 (sinx-tanx)/((sinx)^3)

I've been playing around with trig identities, derivitives, etc. for about a total of 2 hours.. I'm not sure what to do.. please help

 

[stapel]

Turn everything into sines and cosines. Convert the terms in the numerator to the common denominator of "cos(x)".

Simplify the complex fraction. Cancel off the common factor of "sin(x)".

Convert the "sin²(x)" into cosines using the Pythagorean Identity. Factor.

Note that cos(x) - 1 = -1(1 - cos(x)). Cancel a common factor.

You should now have a fraction in only cosine. Evaluate at x = 0.

Eliz.

 

[rragas]

im with you to the very end

when i change

"cosx - 1" into "-1(1-cosx)" i don't think i can cancel it because the denominator is

"1-(cosx)^2"

am i missing something?

 

[pka]

\(\displaystyle 1 - \cos ^2 (x) = \left( {1 - \cos (x)} \right)\left( {1 + \cos (x)} \right)\)

 

[rragas]

eh eh eh.. ya.. thanks :roll: