How Do Trig Identities Help Calculate Derivatives?

[Zeihl]

1. Find the limit of [Cos(x+h)-Cos(x)]/h as h approaches 0



2. Solve using trig identity cos(A+B)= cos(A)cos(B)-sin(A)sin(B)



3. My first class using the actual definition of a derivative. My high school teacher just showed us the shorthand and said "good luck when you get to college"... he was only worried about his AP test scores. Any help appreciated

 

[snipez90]

Well you should know how to start this since there is really only one thing you could apply the cos addition formula to.

 

[Elucidus]

I will mention that somewhere in the middle of working out this problem you will need to know the following facts (that you should have already encountered when discussing limits of trigonometric functions):

$$\lim_{h \rightarrow 0} \frac{\sin h}{h} = 1$$

$$\lim_{h \rightarrow 0} \frac{\cos h - 1}{h} = 0$$

--Elucidus

 

[Zeihl]

Weird, I had edited it earlier with my work, but I suppose the internet messed up when trying to submit.

Anyways, I believe I have it correct, thanks anyways.