# How is sinx/(2sin(x/2)) = cos(x/2)?

1. Oct 9, 2012

### mr0no

1. The problem statement, all variables and given/known data
Prove sinx/(2sin(x/2)) = cos(x/2)
and
(sin(x) cos(x/2^(n+1)))/(2^n(sinx/2^n)) = sinx/(2^(n+1)sin(x/(2^n+1)))

2. Relevant equations

3. The attempt at a solution

2. Oct 9, 2012

### Mentallic

For the first, how do you expand $\sin(2x)$ into terms of sin(x) and cos(x)? Now apply that to the numerator sin(x).

For the second, again apply the same rule.

3. Oct 9, 2012

### SammyS

Staff Emeritus
Hello mr0no. Welcome to PF !

According to the rules for homework help in this Forum, you need to show your work before we can help.

Since you're new here, I'll give you a hint.

For the first one use the double angle identity to write sin(x) in a different manner, by looking at sin(x) as sin(2(x/2)) .

4. Oct 9, 2012

### mr0no

Thanks for giving me a tip instead of solving the whole thing for me. That's just what I need. I guess I will be revising trig identities tomorrow :)