What is the Difference Quotient for f(x) = sin(x)?

[EL ALEM]

Homework Statement

Show that if f(x)=sinx then (f(x+h)-f(x))/h=((sin(h/2))/(h/2))(cos(x+h/2)

Homework Equations

Trig identities, possibly the half angle formulas?

The Attempt at a Solution

(f(x+h)-f(x))/h
= (f(x+ h/2 + h/2)-f(x))/(h/2 + h/2)
= (sin(x+ h/2 + h/2)-sin(x))/(h/2 + h/2)
im stuck after this, don't know what to do..

 

[eumyang]

Hope this isn't too much of a hint, but instead of doing what you have above, I would try to use the sum-to-product identity.

 

[EL ALEM]

Sum to product identity? Thats the first time I've heard of that one, I looked it up on wikipedia and I don't recognize at all, let alone apply it to this problem. Can you help me get started w/ it?

 

[EL ALEM]

Nevermind i got thanks a bunch for showing me that identity!