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Category: Relation and Functions

deveopp-g-x-1-sin-nx-at-fourier-series-x-kpi-n-

Question Number 142229 by mathmax by abdo last updated on 28/May/21 $$\mathrm{deveopp}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{nx}\right)}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{series}\:\left(\mathrm{x}\neq\frac{\mathrm{k}\pi}{\mathrm{n}}\right) \\ $$ Answered by mathmax by abdo last updated on 29/May/21 $$\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{2i}}{\mathrm{e}^{\mathrm{inx}} −\mathrm{e}^{−\mathrm{nx}}…

developpf-x-2-3-cosx-at-fourier-serie-

Question Number 142228 by mathmax by abdo last updated on 28/May/21 $$\mathrm{developpf}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\mathrm{3}+\mathrm{cosx}}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 28/May/21 $$\mathrm{another}\:\mathrm{way}\:\mathrm{f}\:\mathrm{is}\:\mathrm{even}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{a}_{\mathrm{o}} }{\mathrm{2}}\:+\sum_{\mathrm{n}=\mathrm{1}}…

calculate-cos-6-pi-8-cos-6-3pi-8-cos-6-5pi-8-cos-6-7pi-8-

Question Number 76633 by mathmax by abdo last updated on 28/Dec/19 $${calculate}\:{cos}^{\mathrm{6}} \left(\frac{\pi}{\mathrm{8}}\right)+{cos}^{\mathrm{6}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)+{cos}^{\mathrm{6}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)+{cos}^{\mathrm{6}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right) \\ $$ Answered by MJS last updated on 28/Dec/19…

if-E-f-f-R-R-continuous-function-with-f-x-Q-x-R-then-E-

Question Number 11067 by suci last updated on 10/Mar/17 $${if}\:{E}=\left\{{f}\mid{f}:\mathbb{R}\rightarrow\mathbb{R}\:{continuous}\:{function}\:{with}\:{f}\left({x}\right)\in\mathbb{Q},\:\forall{x}\in\mathbb{R}\right\}, \\ $$$${then}\:{E}=….??? \\ $$ Commented by FilupS last updated on 10/Mar/17 $$\mathbb{Q}\:=\:\mathrm{irrational}\:\mathrm{numbers}\:\mathrm{set} \\ $$$$ \\…

If-f-2x-1-g-3-x-x-f-3x-5-x-1-2g-2x-1-x-1-x-x-1-for-every-x-R-x-1-Find-f-x-

Question Number 10987 by Joel576 last updated on 05/Mar/17 $$\mathrm{If}\: \\ $$$$\bullet\:{f}\left(\mathrm{2}{x}\:+\:\mathrm{1}\right)\:+\:{g}\left(\mathrm{3}\:−\:{x}\right)\:=\:{x} \\ $$$$\bullet\:{f}\left(\frac{\mathrm{3}{x}\:+\:\mathrm{5}}{\:{x}\:+\:\mathrm{1}}\right)\:+\:\mathrm{2}{g}\left(\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{{x}\:+\:\mathrm{1}}\right)\:=\:\frac{{x}}{{x}\:+\:\mathrm{1}} \\ $$$$\mathrm{for}\:\mathrm{every}\:{x}\:\in\:\mathbb{R},\:\:{x}\:\neq\:−\mathrm{1} \\ $$$$\mathrm{Find}\:{f}\left({x}\right)\:!! \\ $$ Answered by ajfour last updated…

calculate-tan-3x-interms-of-tanx-

Question Number 76497 by mathmax by abdo last updated on 27/Dec/19 $${calculate}\:{tan}\left(\mathrm{3}{x}\right)\:{interms}\:{of}\:{tanx} \\ $$ Answered by Rio Michael last updated on 27/Dec/19 $${tan}\mathrm{3}{x}\:=\:{tan}\left(\mathrm{2}{x}\:+\:{x}\right)\:=\:\frac{{tan}\mathrm{2}{x}\:+\:{tanx}}{\mathrm{1}−{tan}\mathrm{2}{xtanx}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\frac{\mathrm{2}{tanx}}{\mathrm{1}−{tan}^{\mathrm{2}}…