Question Number 86168 by jagoll last updated on 27/Mar/20 $$\mathrm{given}\: \\ $$$$\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:\mathrm{y}\:=\:\mathrm{2sin}\:\left(\mathrm{x}+\mathrm{y}\right)\: \\ $$$$\mathrm{x}+\mathrm{y}\:\neq\:\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{tan}\:\frac{\mathrm{x}}{\mathrm{2}}\:\mathrm{tan}\:\frac{\mathrm{y}}{\mathrm{2}}\:=\: \\ $$ Answered by john santu last…
Question Number 20631 by Tinkutara last updated on 30/Aug/17 $${Solve}\:{the}\:{inequality} \\ $$$$\left({x}\:+\:\mathrm{3}\right)^{\mathrm{5}} \:−\:\left({x}\:−\:\mathrm{1}\right)^{\mathrm{5}} \:\geqslant\:\mathrm{244}. \\ $$ Answered by mrW1 last updated on 30/Aug/17 $$\mathrm{let}\:\mathrm{u}=\mathrm{x}+\mathrm{1} \\…
Question Number 86167 by jagoll last updated on 27/Mar/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{tan}\:\mathrm{x}}\right)}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$ Commented by mathmax by abdo last updated on 27/Mar/20 $${let}\:{take}\:{a}\:{try} \\…
Question Number 20626 by NECx last updated on 29/Aug/17 Answered by $@ty@m last updated on 30/Aug/17 $$\frac{\mathrm{2}}{{log}_{{a}} {x}}+\frac{\mathrm{1}}{{log}_{{a}} {ax}}+\frac{\mathrm{3}}{{log}_{{a}} {a}^{\mathrm{2}} {x}}=\mathrm{0} \\ $$$$\frac{\mathrm{2}}{{log}_{{a}} {x}}+\frac{\mathrm{1}}{{log}_{{a}} {ax}}+\frac{\mathrm{1}}{{log}_{{a}}…
Question Number 151699 by iloveisrael last updated on 22/Aug/21 $$\:\:\:\:\underset{{x}^{\mathrm{3}} +\mathrm{2022}{x}−\mathrm{2021}=\mathrm{0}} {\sum}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)\:=? \\ $$ Answered by mr W last updated on 22/Aug/21 $${x}^{\mathrm{3}} +\mathrm{2022}{x}−\mathrm{2021}=\mathrm{0} \\…
Question Number 86160 by jagoll last updated on 27/Mar/20 $$\mathrm{If}\:\left(\mathrm{x}−\mathrm{1}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)\: \\ $$ Commented by john santu last updated on 27/Mar/20 $${replace}\:{x}\:{by}\:\frac{\mathrm{1}}{{x}} \\ $$$$\Rightarrow\left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right){f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left({x}\right)=\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{{x}}−\mathrm{1}}…
Question Number 20625 by mondodotto@gmail.com last updated on 29/Aug/17 Commented by $@ty@m last updated on 30/Aug/17 $${it}\:{seems}\:{something}\:{missing}\:{in}\:{the}\: \\ $$$${question}\:{because}\:{in}\:'{if}'\:{part},\:{there} \\ $$$${is}\:'>{c}'\:{but}\:{there}\:{is}\:{no}\:'{c}'\:{in}'{prove}\:{that}'\:{part}. \\ $$ Answered by…
Question Number 20619 by Tinkutara last updated on 29/Aug/17 $${Solve}\:{the}\:{equation}\:{z}^{{n}−\mathrm{1}} \:=\:\bar {{z}}\:\left({n}\:\in\:{N}\right) \\ $$ Answered by ajfour last updated on 29/Aug/17 $$\mid{z}\mid=\mathrm{1}\: \\ $$$$\:{z}^{{n}} =\mid{z}\mid^{\mathrm{2}}…
Question Number 20616 by virus last updated on 29/Aug/17 $${x}={r}\mathrm{cos}\:\theta\mathrm{cos}\:\emptyset,{y}={r}\mathrm{sin}\:\theta\mathrm{sin}\:\emptyset,{z}=\mathrm{sin}\:\theta \\ $$$${then}\:{prove}\:{that}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$ Commented by virus last updated on 01/Sep/17 $${please}\:{solve}\:{this}…
Question Number 151685 by iloveisrael last updated on 22/Aug/21 $$\:\:{Find}\:{maximum}\:{value}\:{of}\:{function} \\ $$$$\:\:\alpha\left({x}\right)=\:\sqrt{\mathrm{2}{x}}\:+\sqrt{\mathrm{16}−{x}}\:+\sqrt{\mathrm{35}+{x}}\:. \\ $$ Answered by mr W last updated on 22/Aug/21 $${x}\geqslant\mathrm{0} \\ $$$${x}\leqslant\mathrm{16}…