Question Number 112645 by bemath last updated on 09/Sep/20 $$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=?\: \\ $$ Answered by john santu last updated on 09/Sep/20 $${let}\:{p}\:=\:\frac{\pi}{\mathrm{7}}\:{and}\:{X}=\mathrm{cos}\:{p}−\mathrm{cos}\:\mathrm{2}{p}+\mathrm{cos}\:\mathrm{3}{p} \\ $$$${multiply}\:{by}\:\mathrm{2sin}\:{p} \\ $$$$\mathrm{2sin}\:{p}\:{X}\:=\:\mathrm{2sin}\:{p}\left(\mathrm{cos}\:{p}−\mathrm{cos}\:\mathrm{2}{p}+\mathrm{cos}\:\mathrm{3}{p}\right)…
Question Number 178182 by mathlove last updated on 13/Oct/22 $$\frac{\mathrm{1}}{{cos}\mathrm{80}}−\frac{\sqrt{\mathrm{3}}}{{sin}\mathrm{80}}=? \\ $$ Commented by cortano1 last updated on 13/Oct/22 $$\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}\:−\frac{\sqrt{\mathrm{3}}}{\mathrm{cos}\:\:\mathrm{10}°}\:=\:\frac{\mathrm{cos}\:\:\mathrm{10}°−\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{10}}{\mathrm{sin}\:\mathrm{10}°\:\mathrm{cos}\:\mathrm{10}°} \\ $$$$\:=\:\frac{\mathrm{4}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{10}°−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{sin}\:\mathrm{10}°\right)}{\mathrm{sin}\:\mathrm{20}°} \\ $$$$\:=\:\frac{\mathrm{4}\left(\mathrm{sin}\:\mathrm{30}°\:\mathrm{cos}\:\mathrm{10}°−\mathrm{cos}\:\mathrm{30}°\:\mathrm{sin}\:\mathrm{10}°\right)}{\mathrm{sin}\:\mathrm{20}°} \\…
Question Number 178153 by mnjuly1970 last updated on 13/Oct/22 Answered by mr W last updated on 13/Oct/22 $$\mathrm{2}=\left(\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{b}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{c}}\right)\geqslant\left(\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)^{\mathrm{3}} \\ $$$$\Rightarrow{a}\geqslant\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}−\mathrm{1}}\:\Rightarrow{a}\geqslant\mathrm{4} \\ $$$$\mathrm{2}=\left(\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{b}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{c}}\right)\leqslant\left(\mathrm{1}+\frac{\mathrm{1}}{{c}}\right)^{\mathrm{3}} \\ $$$$\Rightarrow{c}\leqslant\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}−\mathrm{1}}\:\Rightarrow{c}\leqslant\mathrm{3} \\…
Question Number 178091 by alcohol last updated on 12/Oct/22 $${remainder}\:{when}\:\mathrm{7}^{\mathrm{9}^{\mathrm{9}^{\mathrm{9}^{\mathrm{9}} } } } \:{is}\:{divided}\:{by}\:\mathrm{10}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 178087 by a.lgnaoui last updated on 12/Oct/22 $${un}\:{avion}\:{volant}\:{a}\:{hauteur}\:{h}=\mathrm{4}{km}\:{du}\:{sol} \\ $$$${a}\:{vitesse}\:{supersonic}\:\:\left({v}\right)\: \\ $$$${sachant}\:{que}\:{la}\:{vitesse}\:{du}\:{son}\:{a}\:{la}\: \\ $$$${hauteur}\:{h}\:{est}\:{de}\:\mathrm{300}{m}/{s}\:{et} \\ $$$${que}\:{le}\:{temps}\:{mis}\:{par}\:{le}\:{son}\:{emis}\:{par} \\ $$$${l}\:{avion}\:{depuis}\:{un}\:{point}\left({c}\right)\:{est}\: \\ $$$${cspte}\:{par}\:{une}\:{prrsonne}\:{avec}\:{un} \\ $$$${retard}\:{de}\:\mathrm{3}{s} \\…
Question Number 112542 by bobhans last updated on 08/Sep/20 $$\mathrm{If}\:\mathrm{7}\:\mathrm{sin}\:\mathrm{y}\:=\:\mathrm{8}\:\mathrm{sin}\:\left(\mathrm{y}+\mathrm{45}°\right).\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\left(\mathrm{y}+\mathrm{45}°\right)\:? \\ $$ Answered by bemath last updated on 08/Sep/20 $$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{y}+\mathrm{45}°\:;\:\mathrm{y}\:=\:\mathrm{x}−\mathrm{45}° \\ $$$$\Leftrightarrow\:\mathrm{7}\:\mathrm{sin}\:\left(\mathrm{x}−\mathrm{45}°\right)\:=\:\mathrm{8}\:\mathrm{sin}\:\mathrm{x} \\ $$$$\Leftrightarrow\:\mathrm{7}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}.\mathrm{sin}\:\mathrm{x}−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}.\mathrm{cos}\:\mathrm{x}\right)\:=\:\mathrm{8sin}\:\mathrm{x} \\…
Question Number 46944 by Tawa1 last updated on 02/Nov/18 Commented by maxmathsup by imad last updated on 03/Nov/18 $${we}\:{have}\:\frac{{x}}{{y}}\:+\frac{{y}}{{x}}\:=\frac{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{{xy}}\:\:{and} \\ $$$$\frac{{x}}{{sin}\theta}\:=\frac{{y}}{{cos}\theta}\:\Rightarrow\frac{{x}^{\mathrm{4}} }{{sin}^{\mathrm{4}} \theta}\:=\frac{{y}^{\mathrm{4}}…
Question Number 112466 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by 1549442205PVT last updated on 08/Sep/20 $$\mid\mathrm{cosx}\mid\geqslant\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \mathrm{x}\Leftrightarrow\mid\mathrm{cosx}\mid\geqslant\mathrm{cos}^{\mathrm{2}} \mathrm{x}=\mid\mathrm{cosx}\mid^{\mathrm{2}} \\ $$$$\Leftrightarrow\mid\mathrm{cosx}\mid\leqslant\mathrm{1}.\mathrm{The}\:\mathrm{last}\:\mathrm{inequality}\:\mathrm{is}\: \\ $$$$\mathrm{always}\:\mathrm{true}\:\forall\mathrm{x}.\mathrm{Hence},\mid\mathrm{cosx}\mid\geqslant\mathrm{1}−\mathrm{sin}^{\mathrm{2}}…
Question Number 177964 by mathlove last updated on 11/Oct/22 $$\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$ Commented by cortano1 last updated on 11/Oct/22 $$\:\frac{\mathrm{cos}\:\mathrm{15}°}{\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{15}°}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}\:\mathrm{cot}\:\mathrm{15}°=\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}×\left(\mathrm{2}+\sqrt{\mathrm{3}}\right) \\ $$$$=\:\frac{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{3}}}\:=\mathrm{2}+\frac{\mathrm{4}\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$$\left(\bullet\right)\:\mathrm{tan}\:\mathrm{15}°=\frac{\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}}{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}} \\…
Question Number 177914 by mathlove last updated on 11/Oct/22 $$\left(\mathrm{1}\right)\:\:\:\:\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{4}{sin}\mathrm{13}\:{cos}\mathrm{13}}=? \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 11/Oct/22 $$\left(\mathrm{1}\right)\:\:\:\:\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{4}{sin}\mathrm{13}\:{cos}\mathrm{13}}=? \\ $$$$\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{2}{sin}\mathrm{26}\:}−\mathrm{1}+\mathrm{1} \\…