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Question 1
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If $\prod ^n_{i=1}\tan ({{\alpha}}_i)=1\, \forall{{\alpha}}_i\, \in\Bigg{[}0,\, \frac{\pi}{2}\Bigg{]}$ where i=1,2,3,...,n. Then maximum value of $\prod ^n_{i=1}\sin ({{\alpha}}_i)$.
A.
$\frac{1}{2^n}$
B.
$\frac{1}{2^{n/2}}$
C.
1
D.
None of these
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