Question Number 213084 by MATHEMATICSAM last updated on 30/Oct/24 $$\mathrm{If}\:\mathrm{0}\:<\:{x}\:<\:\frac{\pi}{\mathrm{2}}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{sin}\left(\mathrm{cos}{x}\right)\:<\:\mathrm{cos}{x}\:<\:\mathrm{cos}\left(\mathrm{sin}{x}\right). \\ $$$$\mathrm{not}\:\mathrm{using}\:\mathrm{graph}. \\ $$ Answered by issac last updated on 30/Oct/24 $${x}=\mathrm{acos}\left({z}\right)\:,\:{z}\in\left[\mathrm{0},\mathrm{1}\right] \\…
Question Number 213119 by a.lgnaoui last updated on 30/Oct/24 $$\mathrm{determiner}\:\boldsymbol{\mathrm{a}}\:\mathrm{et}\:\boldsymbol{\mathrm{b}}\:\mathrm{par}\:\:\:;\:\:\mathrm{AB}\:\bot\mathrm{BC} \\ $$$$\begin{cases}{\mathrm{AM}\:=\mathrm{5}}\\{\mathrm{AC}\:\:=\mathrm{16}}\end{cases} \\ $$ Commented by a.lgnaoui last updated on 30/Oct/24 Answered by A5T last…
Question Number 213054 by 281981 last updated on 29/Oct/24 Commented by Ghisom last updated on 30/Oct/24 $$\mathrm{in}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{and}\:\mathrm{its}\:\mathrm{circumcircle} \\ $$$$\mathrm{is} \\ $$$$\mathrm{1}:\frac{\mathrm{4}\pi\sqrt{\mathrm{3}}}{\:\mathrm{9}}\:\approx\:\mathrm{1}:\mathrm{2}.\mathrm{4} \\ $$$$\mathrm{here}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{is}…
Question Number 213063 by a.lgnaoui last updated on 29/Oct/24 $$\mathrm{Area}\:\mathrm{of}\:\left[\mathrm{ACBD}\right]\:\:? \\ $$$$\left\{\mathrm{A}\:,\mathrm{B}\:\right\}\in\:\mathrm{elipse}\:\mathrm{verticale}\:\: \\ $$$$\left[\mathrm{AB}\right]\bot\mathrm{MC} \\ $$$$\mathrm{M}\in\:\mathrm{elipse}\:\mathrm{horizontale}\:\: \\ $$$$\mathrm{A}\:\in\left[\mathrm{elipse}\:\mathrm{horizontale}\:\cap\mathrm{elipse}\:\mathrm{veeticale}\right]. \\ $$ Commented by a.lgnaoui last updated…
Question Number 212777 by Ghisom last updated on 23/Oct/24 $$\mathrm{question}\:\mathrm{212462} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{25}{x}^{\mathrm{2}} +\mathrm{160}}}=\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{95}{x}^{\mathrm{2}} +\mathrm{2560}}} \\ $$$$ \\…
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Question Number 212569 by a.lgnaoui last updated on 17/Oct/24 $$\mathrm{Axis}\:\mathrm{of}\:\mathrm{C},\mathrm{P},\mathrm{N}\:\mathrm{then}\:\mathrm{concluat}\:\mathrm{for} \\ $$$$\mathrm{Area}\left[\:\mathrm{OPN}\right]\:;\:\mathrm{ON}:\mathrm{tangente}\:\mathrm{au}\:\mathrm{cercle} \\ $$ Commented by a.lgnaoui last updated on 17/Oct/24 Terms of Service Privacy…
Question Number 212557 by tri26112004 last updated on 17/Oct/24 Answered by Ghisom last updated on 17/Oct/24 $$\mathrm{cos}\:{x}\:={c} \\ $$$$\mathrm{sin}\:{x}\:=\sqrt{\mathrm{1}−{c}^{\mathrm{2}} } \\ $$$$\left(\sqrt{\mathrm{1}−{c}^{\mathrm{2}} }\right)^{\mathrm{8}} +{c}^{\mathrm{8}} =…
Question Number 212524 by alcohol last updated on 16/Oct/24 Commented by York12 last updated on 16/Oct/24 $$\mathrm{What}\:\mathrm{is}\:\mathrm{that}\:\mathrm{textbook} \\ $$ Commented by alcohol last updated on…
Question Number 212477 by Durganand last updated on 14/Oct/24 Answered by mehdee7396 last updated on 14/Oct/24 $$\frac{{sin}\mathrm{2}{acosa}−{sinacos}\mathrm{2}{a}}{{sin}\mathrm{2}{asina}} \\ $$$$=\frac{{sina}}{{sin}\mathrm{2}{asina}}=\frac{\mathrm{1}}{{sin}\mathrm{2}{a}}\:\:\checkmark \\ $$ Answered by A5T last…