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Category: Trigonometry

If-0-lt-x-lt-pi-2-then-prove-sin-cosx-lt-cosx-lt-cos-sinx-not-using-graph-

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-213054

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}…

Area-of-ACBD-A-B-elipse-verticale-AB-MC-M-elipse-horizontale-A-elipse-horizontale-elipse-veeticale-

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-212462-prove-that-0-dx-x-4-25x-2-160-0-dx-x-4-95x-2-2560-my-attempt-but-is-it-a-proof-I-b-a-0-dx-x-4-ax-2-b-2-pi-b-1-4-agm-1

Question Number 212777 by Ghisom last updated on 23/Oct/24 $$\mathrm{question}\:\mathrm{212462} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{25}{x}^{\mathrm{2}} +\mathrm{160}}}=\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{95}{x}^{\mathrm{2}} +\mathrm{2560}}} \\ $$$$ \\…

Question-212477

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…