Help w/ the difference quotient

[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..

 

[EL ALEM]

Ok so I used the sum to product identity and ended up w/ this

(2sin(h/2)cos((2x+h)/2))/h

not sure how to simplify it further

NM got it.