s(x) = sinx

Limit (sin(x+h) - sinx)/h

siny - sinx = 2sin(y-x)/2 (cos(y+x))/2

Let y=x+h

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

My problem is I cant figure out how he got the left side of the last equation. I see where the cos(x + (h/2)) is coming from.

Question

s(x) = sinx

Limit (sin(x+h) - sinx)/h 

siny - sinx = 2sin(y-x)/2 (cos(y+x))/2

Let y=x+h

sin(h/2)/(h/2)(cos(x + (h/2))

My problem is I cant figure out how he got the left side of the last equation. I see where the cos(x + (h/2)) is coming from.

anonymous · Answer

can you post a screen shot?

anonymous · Answer

I guess I could try. This is a proof of sinx/x = 1

anonymous · Answer

Let me know if the text is too small.

anonymous · Answer

yeah that is usually done by something called the "squeeze theorem"  have never seen this approach before but i bet your question is algebra based

anonymous · Answer

It's using trig identities and to be honest I haven't studied much trig

anonymous · Answer

yeah it is an algebra question you are asking

anonymous · Answer

the input for cosine in one line is $\frac{y+x}{2}$
then they wrote 
put $y=x+h$
that makes 
$$\frac{y+x}{2}=\frac{x+h+x}{2}=\frac{2x+h}{2}=x+\frac{h}{2}$$ algebra for all of that

anonymous · Answer

Yeah, I figured out what he was doing with Cos, I just cant figure out how he got sin(h/2)/(h/2)