1. Verifying

Verify for all integers $n$,

$\cos {\frac {(2n+1)\pi}{2}}=0$.

Help? I know the double angle, half-angle, and sum and difference formulas, but I can't figure out how to verify it.

2. Hello,
Originally Posted by chrozer
Verify for all integers $n$,

$\cos {\frac {(2n+1)\pi}{2}}=0$.

Help? I know the double angle, half-angle, and sum and difference formulas, but I can't figure out how to verify it.
You can do it by induction.

Or... :

$\cos \frac{(2n+1)\pi}{2}=\cos(n \pi+\tfrac \pi 2)$
use the sum formula.

Then remember that $\sin(n \pi)=0$

3. Originally Posted by Moo
Hello,

You can do it by induction.

Or... :

$\cos \frac{(2n+1)\pi}{2}=\cos(n \pi+\tfrac \pi 2)$
use the sum formula.

Then remember that $\sin(n \pi)=0$
Thanks.