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

[mr0no]

Homework Statement

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)))

Homework Equations

The Attempt at a Solution

 

[Mentallic]

Homework Statement

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)))

Homework Equations

The Attempt at a Solution

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.

 

[SammyS]

Homework Statement

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)))

Homework Equations

The Attempt at a Solution

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)) .

 

[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 :)