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Question Number 30742 by abdo imad last updated on 25/Feb/18

p r o v e t h a t \forall p \in N i t e x i s t o n e p o l y n o m i a l Q_{2 p} /

s i n (2 p + 1) θ = {s i n}^{2 p + 1} θ Q_{2 p} (c o t a n θ) a n d {d e g Q}_{2 p} = 2 p

2) p r o v e t h a t \prod_{k = 1}^{p} t a n (\frac{k π}{2 p + 1}) = \sqrt{2 p + 1} .