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Category: Relation and Functions

prove-the-relations-1-t-0-1-arctan-1-t-2-t-arccost-2-t-1-1-2-arccos-1-t-2-arccost-

Question Number 40107 by maxmathsup by imad last updated on 15/Jul/18 $${prove}\:{the}\:{relations} \\ $$$$\left.\mathrm{1}\left.\right)\left.\:\forall{t}\:\in\right]\mathrm{0},\mathrm{1}\right]\:\:\:{arctan}\left(\frac{\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{{t}}\right)={arccost} \\ $$$$\left.\mathrm{2}\right)\:\forall\:{t}\in\left[−\mathrm{1},\mathrm{1}\right]\:\:\:\:\mathrm{2}\:{arccos}\sqrt{\frac{\mathrm{1}+{t}}{\mathrm{2}}}\:={arccost} \\ $$ Answered by math khazana by abdo…

let-f-x-x-1-1-x-2-n-study-tbe-derivability-of-f-at-points-0-and-1-n-natural-integr-

Question Number 40102 by maxmathsup by imad last updated on 15/Jul/18 $${let}\:{f}\left({x}\right)\:=\:\frac{\mid{x}\mid}{\left(\mathrm{1}+\mid\mathrm{1}−{x}^{\mathrm{2}} \mid\right)^{{n}} } \\ $$$${study}\:{tbe}\:{derivability}\:{of}\:{f}\:{at}\:{points}\:\mathrm{0}\:{and}\:\mathrm{1}\:\left({n}\:{natural}\:{integr}\right) \\ $$ Answered by math khazana by abdo last…