Question Number 86041 by M±th+et£s last updated on 26/Mar/20 $$\left.\mathrm{1}\right){if}\: \\ $$$${sin}\left(\theta−{x}\right)={k}\:{sin}\left(\theta+\alpha\right) \\ $$$${find}\:{tan}\left(\theta\right)\:{and}\:{k} \\ $$$$ \\ $$$${then}\:{find}\:\theta\:{in}\left[\mathrm{0},\mathrm{2}\pi\right]\:\:{when}\:{k}=\frac{\mathrm{1}}{\mathrm{2}}\:{and}\:\alpha=\pi \\ $$$$ \\ $$$$\left.\mathrm{2}\right){if}\:{x}={sin}\left({t}\right)\:\:{and}\:\:{y}={cos}\left(\mathrm{2}{t}\right) \\ $$$${show}\:{that} \\…
Question Number 151568 by tabata last updated on 21/Aug/21 $$\int\:\sqrt{{sec}\left({x}\right)+{tan}\left({x}\right)}\:{dx} \\ $$$$ \\ $$$${how}\:{can}\:{it}\:{solve} \\ $$ Answered by puissant last updated on 22/Aug/21 $$=\int\sqrt{\frac{\mathrm{1}}{{cosx}}+\frac{{sinx}}{{cosx}}}{dx} \\…
Question Number 86024 by MJS last updated on 26/Mar/20 $$\mathrm{last}\:\mathrm{three}\:\mathrm{digits}\:\mathrm{of} \\ $$$$\mathrm{951413}^{\mathrm{314159}} =? \\ $$ Commented by naka3546 last updated on 26/Mar/20 $$\mathrm{277} \\ $$…
Question Number 86025 by Maclaurin Stickker last updated on 26/Mar/20 $${find}\:{the}\:{three}\:{last}\:{digits}\:{of}\:\:\mathrm{7}^{\mathrm{2020}} . \\ $$ Commented by MJS last updated on 26/Mar/20 $$\mathrm{you}\:\mathrm{can}\:\mathrm{do}\:\mathrm{it}\:\mathrm{yourself}.\:\mathrm{find}\:\mathrm{out},\:\mathrm{after}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{steps}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{repeat} \\…
Question Number 86018 by Maclaurin Stickker last updated on 26/Mar/20 $${Find}\:{the}\:{three}\:{last}\:{digits}\:{of}\:\mathrm{5}^{\mathrm{9999}} . \\ $$ Answered by MJS last updated on 26/Mar/20 $$\mathrm{5}^{\mathrm{1}} \:\:\:\:\:\mathrm{005} \\ $$$$\mathrm{5}^{\mathrm{2}}…
Question Number 85961 by A8;15: last updated on 26/Mar/20 Commented by MJS last updated on 26/Mar/20 $$\mathrm{we}\:\mathrm{still}\:\mathrm{do}\:\mathrm{not}\:\mathrm{know}\:\mathrm{what}\:{V}_{{a}} ^{{b}} \:\mathrm{is} \\ $$ Commented by jagoll last…
Question Number 151486 by mathocean1 last updated on 21/Aug/21 $$\int{ln}\left({sinx}\right)=?\: \\ $$$${x}\:\neq\:\mathrm{0}\:+\:\mathrm{2}{k}\pi\:;\:{k}\:\in\:\mathbb{Z} \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\mathrm{ln}\left(\mathrm{sin}{x}\right)\:{dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:{x}\mathrm{ln}\left(\mathrm{sin}{x}\right)−\int{x}\mathrm{cot}{x}\:{dx} \\…
Question Number 85935 by A8;15: last updated on 26/Mar/20 Commented by john santu last updated on 26/Mar/20 $${i}\:{don}'{t}\:{understand}\:{your}\:{question} \\ $$ Commented by MJS last updated…
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Question Number 20364 by mondodotto@gmail.com last updated on 26/Aug/17 Answered by Tinkutara last updated on 26/Aug/17 $$\mathrm{59}\:=\:\mathrm{77}\:−\:\left(\mathrm{6}\:+\:\mathrm{3}{x}\right)\:+\:{x} \\ $$$$\mathrm{2}{x}\:=\:\mathrm{12} \\ $$$${x}\:=\:\mathrm{6} \\ $$ Commented by…