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Question-60873

Question Number 60873 by Kunal12588 last updated on 26/May/19 Commented by Prithwish sen last updated on 26/May/19 $$\left.\mathrm{i}\right)\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{4x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}\right)−\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\:>\mathrm{0} \\ $$$$\frac{\mathrm{4x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}}…

If-tanA-3-prove-it-3-sinA-cosA-3-4-

Question Number 126405 by amns last updated on 20/Dec/20 $$\boldsymbol{\mathrm{If}}\:{tanA}\:=\:\sqrt{\mathrm{3}}\:,\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{it}}:\:\sqrt{\mathrm{3}}\:{sinA}\:{cosA}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$ Commented by amns last updated on 20/Dec/20 $$\mathrm{help}\:\mathrm{me},\:\mathrm{plz}… \\ $$ Commented by som(math1967)…

For-all-in-0-pi-2-show-that-cos-sin-sin-cos-

Question Number 60849 by Kunal12588 last updated on 26/May/19 $${For}\:{all}\:\theta\:{in}\:\left[\mathrm{0},\:\pi/\mathrm{2}\right]\:{show}\:{that}\:{cos}\left({sin}\theta\right)\geqslant{sin}\left({cos}\theta\right). \\ $$ Commented by Prithwish sen last updated on 26/May/19 $$\mathrm{when}\:\theta\in\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\:\right] \\ $$$$\mathrm{sin}\theta\:\mathrm{and}\:\mathrm{cos}\theta\:\mathrm{lies}\:\mathrm{between}\:\mathrm{0}\:\mathrm{to}\:\mathrm{1} \\ $$$$\therefore\:\mathrm{For}\:\alpha\in\left[\mathrm{0},\mathrm{1}\right]…

Prove-or-disprove-that-there-is-a-positive-integer-suitable-for-n-3-1-n-n-is-divided-by-n-3-1-n-Z-

Question Number 60808 by naka3546 last updated on 26/May/19 $${Prove}\:\:{or}\:\:{disprove}\:\:{that}\:\:{there}\:\:{is} \\ $$$${a}\:\:{positive}\:\:{integer}\:\:{suitable}\:\:{for} \\ $$$$\:\:\:\:\:\:\:{n}^{\mathrm{3}} \:+\:\mathrm{1}\:\:\:\mid\:\:\:{n}!\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:{n}!\:\:\:{is}\:\:{divided}\:\:{by}\:\:{n}^{\mathrm{3}} \:+\:\mathrm{1}\:\:\right) \\ $$$${n}\:\:\in\:\:\mathbb{Z}^{+} \\ $$ Commented by mr W last…