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sin-50-sin-40-without-tables-or-calculators-

Question Number 73787 by Rio Michael last updated on 15/Nov/19 $${sin}\:\mathrm{50}\:+\:{sin}\:\mathrm{40}=\:?\:{without}\:{tables}\:{or}\:{calculators} \\ $$ Commented by mind is power last updated on 15/Nov/19 $$\mathrm{i}\:\mathrm{see}\:\mathrm{just}\:\mathrm{cardan}\:\mathrm{Methode} \\ $$$$\mathrm{sin}\left(\mathrm{50}\right)=\mathrm{sin}\left(\mathrm{90}−\mathrm{40}\right)=\mathrm{cos}\left(\mathrm{40}\right)…

hello-show-that-n-1-1-n-nsin-n-1-n-2-pie-1-pie-1-2e-pi-2e-pi-indication-Residus-Theorem-let-f-z-zsin-z-1-z-2-sin-piz-have-a-very-nice-day-

Question Number 73774 by mind is power last updated on 15/Nov/19 $$\mathrm{hello}\:,\mathrm{show}\:\mathrm{that} \\ $$$$\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{nsin}\left(\mathrm{n}\right)}{\mathrm{1}+\mathrm{n}^{\mathrm{2}} }=\frac{\pi\mathrm{e}^{\mathrm{1}} −\pi\mathrm{e}^{−\mathrm{1}} }{−\mathrm{2e}^{\pi} +\mathrm{2e}^{−\pi} } \\ $$$$\mathrm{indication}\:,\mathrm{Residus}\:\mathrm{Theorem}\:\mathrm{let} \\ $$$$\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{zsin}\left(\mathrm{z}\right)}{\left(\mathrm{1}+\mathrm{z}^{\mathrm{2}}…

3000000-3000000-4000000-4000000-

Question Number 139278 by Agnibhoo last updated on 25/Apr/21 $$\sqrt{\frac{\mathrm{3000000}\:+\:\mathrm{3000000}}{\mathrm{4000000}\:+\:\mathrm{4000000}}}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 25/Apr/21 $$\sqrt{\frac{\mathrm{6}×\cancel{\mathrm{1000000}}}{\mathrm{8}×\cancel{\mathrm{1000000}}}}=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$ Commented by otchereabdullai@gmail.com…