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Question Number 30486 by abdo imad last updated on 22/Feb/18
$${let}\:{give}\:{a}_{{n}} =\:\prod_{{k}=\mathrm{1}} ^{{n}} \:{cos}\left(\:\frac{\pi}{\left({k}+\mathrm{2}\right)!}\right)\:{and} \\ $$$${b}_{{n}} =\prod_{{k}=\mathrm{1}} ^{{n}} \:\:{sin}\left(\frac{\pi}{\left({k}+\mathrm{2}\right)!}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{foe}\:{a}_{{n}} \:{and}\:{b}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{a}_{{n}} .{b}_{{n}} . \\ $$