Question Number 135034 by mnjuly1970 last updated on 09/Mar/21 $$\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}\:\: \\ $$$$\:\:\:\:{if}\:\:{n}\geqslant\mathrm{2}\:\:\:{and}\:\:\:{P}_{{n}} =\underset{{n}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}{sin}\left(\frac{{k}\pi}{{n}}\right) \\ $$$$\:\:\:\:\:{find}\:::\:{lim}_{{n}\rightarrow\infty} \frac{{nP}_{{n}} }{\mathrm{2}}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\:\frac{\pi}{\mathrm{3}}} \frac{{cos}\left(\mathrm{3}{x}\right)}{{sin}^{{n}} \left({x}\right)}{dx} \\ $$ Terms…
Question Number 69494 by TawaTawa last updated on 24/Sep/19 Commented by TawaTawa last updated on 24/Sep/19 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{find}\:\mathrm{the}\:\mathrm{Area}\:\mathrm{and}\:\mathrm{Perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{part}. \\ $$ Commented by mind is power last…
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Question Number 135024 by mr W last updated on 09/Mar/21 Commented by mr W last updated on 09/Mar/21 $${an}\:{unsolved}\:{old}\:{question} \\ $$ Commented by mr W…
Question Number 3950 by Rasheed Soomro last updated on 25/Dec/15 $$\mathcal{W}{e}\:{can}\:{make}\:{a}\:\boldsymbol{{cyllinder}}\:{from}\:{a} \\ $$$$\boldsymbol{{rectangle}}\:{by}\:{connecting}\:{its}\:{opposite} \\ $$$$\boldsymbol{{edges}}. \\ $$$${Suppose}\:{we}\:{have}\:{two}\:{copies}\:{of}\:{a} \\ $$$$\boldsymbol{{non}}−\boldsymbol{{square}}\:\boldsymbol{{rectangle}}.{From} \\ $$$${one}\:{copy}\:{we}\:{make}\:{a}\:{long}\:{cyllinder} \\ $$$${by}\:{connecting}\:{long}\:{edges}\:{of}\:{it}\: \\ $$$${whereas}\:{from}\:{other}\:{copy}\:{by}\:{connecting}…
Question Number 69482 by Henri Boucatchou last updated on 24/Sep/19 $$\underset{{n}\rightarrow\infty} {{lim}}\frac{\mathrm{2}+{cosn}}{\mathrm{4}{n}+{sinn}}\:=\:? \\ $$ Commented by Tony Lin last updated on 24/Sep/19 $$−\mathrm{1}\leqslant{cosn}\leqslant\mathrm{1} \\ $$$$\mathrm{1}\leqslant\mathrm{2}+{cosn}\leqslant\mathrm{3}…
Question Number 135019 by faysal last updated on 09/Mar/21 Answered by Dwaipayan Shikari last updated on 09/Mar/21 $${sin}\mathrm{6}°{sin}\mathrm{42}°{sin}\mathrm{66}°{sin}\mathrm{78}° \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left({cos}\mathrm{60}°−{cos}\mathrm{72}°\right)\left({cos}\mathrm{36}°−{cos}\mathrm{120}°\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}\right)\left(\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{3}−\sqrt{\mathrm{5}}}{\mathrm{4}}\right)\left(\frac{\sqrt{\mathrm{5}}+\mathrm{3}}{\mathrm{4}}\right)=\frac{\mathrm{1}}{\mathrm{16}}=\Lambda \\ $$$${cos}\mathrm{6}°{cos}\mathrm{42}°{cos}\mathrm{66}°{cos}\mathrm{78}° \\…
Question Number 3944 by Rasheed Soomro last updated on 25/Dec/15 $$\mathcal{P}{rove}\:{that},\:{inside}\:\:{a}\:{given}\:{square},\:{a}\:{semicircle}\: \\ $$$${of}\:{the}\:{largest}\:{possible}\:{area},\:{can}\:{be}\:{constructed}\: \\ $$$${using}\:{ruler}\:{and}\:{compass}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69478 by Henri Boucatchou last updated on 24/Sep/19 $$\:\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}sin}}\left(\boldsymbol{{n}\pi}\right)\:=\:? \\ $$ Commented by mathmax by abdo last updated on 24/Sep/19 $${sin}\left({n}\pi\right)=\mathrm{0}\:\Rightarrow{lim}_{{n}\rightarrow+\infty} {sin}\left({n}\pi\right)=\mathrm{0}…
Question Number 3943 by Rasheed Soomro last updated on 25/Dec/15 $$\mathcal{W}{hat}\:{is}\:{the}\:{area}\:\:{of}\:\:{overlapping}\:{region} \\ $$$${of}\:{three}\:{circles}\:{of}\:{radii}\:\boldsymbol{\mathrm{r}}_{\mathrm{1}} \:,\:\boldsymbol{\mathrm{r}}_{\mathrm{2}} \:,\:\boldsymbol{\mathrm{r}}_{\mathrm{3}} \:{with}\:{their} \\ $$$${respective}\:{centres}\:\boldsymbol{\mathrm{C}}_{\mathrm{1}} \:,\:\boldsymbol{\mathrm{C}}_{\mathrm{2}} \:{and}\:\boldsymbol{\mathrm{C}}_{\mathrm{3}} \:{when} \\ $$$$\boldsymbol{\mathrm{r}}_{\mathrm{1}} +\boldsymbol{\mathrm{r}}_{\mathrm{2}} >\:\boldsymbol{\mathrm{C}}_{\mathrm{1}}…