Verify for all integers $\displaystyle n$, $\displaystyle \cos {\frac {(2n+1)\pi}{2}}=0$. Help? I know the double angle, half-angle, and sum and difference formulas, but I can't figure out how to verify it.
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Hello, Originally Posted by chrozer Verify for all integers $\displaystyle n$, $\displaystyle \cos {\frac {(2n+1)\pi}{2}}=0$. 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... : $\displaystyle \cos \frac{(2n+1)\pi}{2}=\cos(n \pi+\tfrac \pi 2)$ use the sum formula. Then remember that $\displaystyle \sin(n \pi)=0$
Originally Posted by Moo Hello, You can do it by induction. Or... : $\displaystyle \cos \frac{(2n+1)\pi}{2}=\cos(n \pi+\tfrac \pi 2)$ use the sum formula. Then remember that $\displaystyle \sin(n \pi)=0$ Thanks.
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