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#### sbhatnagar

##### Active member

- Jan 27, 2012

- 95

__Challenge Problem__If $A=\dfrac{\pi}{2^{n+1}}$ and $B=\dfrac{\pi}{2^{n+2}}$, prove that

\[\prod_{r=0}^n (\cos 2^r A + \cos 2^r B)=\frac{1}{2^{n+1}\left( \cos \frac{\pi}{2^{n+2}}-\cos \frac{\pi}{2^{n+1}}\right)}\]

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