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Question Number 108644 by bemath last updated on 18/Aug/20 $$\:\:\:\frac{{bemath}}{\bigstar} \\ $$$${find}\:{the}\:{value}\:{of}\: \\ $$$$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)?\: \\ $$ Commented by bemath last updated on 18/Aug/20 $${great}\:{answer}\:{all}\:{master} \\…
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Question Number 173983 by mnjuly1970 last updated on 23/Jul/22 $$ \\ $$$$\:\:\:{in}\:{A}\overset{\Delta} {{B}C}\:\:{prove}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\:{cos}\left({A}\:\right)}{{a}^{\:\mathrm{3}} }\:+\frac{{cos}\left({B}\right)}{{b}^{\:\mathrm{3}} }\:+\frac{{cos}\left({C}\right)}{{c}^{\:\mathrm{3}} }\:\geqslant\frac{\mathrm{81}}{\mathrm{16}{p}^{\:\mathrm{3}} } \\ $$$$\:\:\:{where}\::\:\:{p}=\:\left({a}+{b}\:+{c}\:\right)/\mathrm{2} \\ $$$$…
Question Number 173893 by azadsir last updated on 20/Jul/22 $$\mathrm{if}\:\int\left(\mathrm{x}\right)\:=\:\mathrm{sinx}\:\mathrm{than}\:\mathrm{prove}\:\mathrm{that}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left\{\int\left(\mathrm{x}\right)^{\mathrm{4}} \right\}\:+\:\left\{\int\left(\mathrm{x}\right)\right\}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$ Commented by MJS_new last updated on 20/Jul/22 $$\int\:\mathrm{is}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{sign}… \\…
Question Number 173894 by azadsir last updated on 20/Jul/22 $$\mathrm{If}\:\:\mathrm{secA}\:−\:\mathrm{tanA}\:=\:\mathrm{Q}\:\mathrm{than}\:\mathrm{prove}\:\mathrm{that},\: \\ $$$$\:\:\:\:\:\:\:\mathrm{cosecA}\:=\:\frac{\mathrm{1}\:+\:\mathrm{Q}^{\mathrm{2}} }{\mathrm{1}\:−\:\mathrm{Q}^{\mathrm{2}} }\: \\ $$ Commented by cortano1 last updated on 20/Jul/22 $${Q}=\frac{\mathrm{1}−\mathrm{sin}\:{A}}{\mathrm{cos}\:{A}}\:\Rightarrow{Q}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}}…
Question Number 173888 by azadsir last updated on 20/Jul/22 $$\mathrm{Prove}\:\mathrm{that},\:\frac{\mathrm{13x}}{\mathrm{x}^{\mathrm{2}} −\sqrt{\mathrm{13x}}+\mathrm{1}}\:=\:\sqrt{\mathrm{13}}\:\mathrm{if},\:\mathrm{x}\:=\:\sqrt{\mathrm{13}}\:+\:\mathrm{2}\sqrt{\mathrm{3}}\: \\ $$ Answered by a.lgnaoui last updated on 20/Jul/22 $$ \\ $$$$\frac{\mathrm{13}{x}}{\left({x}^{\mathrm{2}} −\sqrt{\mathrm{13}}{x}+\mathrm{1}\right)}=\frac{\mathrm{13}{x}}{\:\sqrt{\mathrm{13}}{x}}\Rightarrow{x}^{\mathrm{2}} −\sqrt{\mathrm{13}}{x}+\mathrm{1}=\sqrt{\mathrm{13}}{x}…