# Verifying

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• February 28th 2009, 10:14 AM
chrozer
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.
• February 28th 2009, 10:17 AM
Moo
Hello,
Quote:

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 $\sin(n \pi)=0$
• February 28th 2009, 11:28 AM
chrozer
Quote:

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.