Category: Others

Question Number 124302 by Dwaipayan Shikari last updated on 02/Dec/20 $${n}=\mathrm{2}^{{n}−\mathrm{1}} {sin}\left(\frac{\pi}{{n}}\right){sin}\left(\frac{\mathrm{2}\pi}{{n}}\right)….{sin}\left(\frac{{n}−\mathrm{1}}{{n}}\pi\right)\:\:{prove}\: \\ $$$$ \\ $$ Answered by mnjuly1970 last updated on 02/Dec/20 $${solution} \\…

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Question Number 58675 by ajfour last updated on 27/Apr/19 Commented by ajfour last updated on 27/Apr/19 $$\mathrm{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{square};\:\mathrm{while},\:\mathrm{PQM}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{sector}.\:\mathrm{Find}\:\mathrm{in}\:\mathrm{what}\:\mathrm{proportion} \\ $$$$\mathrm{are}\:\mathrm{radii}\:\mathrm{b},\:\mathrm{r},\:\mathrm{g}\:\left(\mathrm{blue},\:\mathrm{red},\:\mathrm{green}\right. \\ $$$$\left.\mathrm{respectively}\right). \\ $$…

Question Number 124178 by Dwaipayan Shikari last updated on 01/Dec/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\:\sqrt{{cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}} {x}}}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 01/Dec/20…