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Author: Tinku Tara

Question-11166

Question Number 11166 by chux last updated on 14/Mar/17 Commented by ridwan balatif last updated on 15/Mar/17 $$\mathrm{cos4}\theta=\mathrm{cos}\left(\mathrm{2}\theta+\mathrm{2}\theta\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2cos}^{\mathrm{2}} \mathrm{2}\theta−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\left\{\mathrm{cos}\left(\theta+\theta\right)\right\}^{\mathrm{2}} −\mathrm{1} \\…

Question-142232

Question Number 142232 by liberty last updated on 28/May/21 Answered by MJS_new last updated on 28/May/21 $$\mathrm{1}.\:{x}=\mathrm{0} \\ $$$$\Rightarrow\:{y}^{\mathrm{3}} =\mathrm{1}\wedge{y}^{\mathrm{4}} −{y}=\mathrm{0}\:\Rightarrow\:{y}=\mathrm{1}\vee{y}=−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i} \\ $$$$\mathrm{2}.\:{y}=\mathrm{0}\:…\:\Rightarrow\:{x}=\mathrm{1}\vee{x}=−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i} \\ $$$$\mathrm{3}.\:{y}={x}\:…\:\Rightarrow\:{x}={y}=\mathrm{1}\vee{x}={y}=−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i}…

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}}…

f-x-2-1-x-2-x-2-f-x-

Question Number 11151 by suci last updated on 14/Mar/17 $${f}\left({x}\right)=\mathrm{2}^{\frac{\mathrm{1}−{x}}{\mathrm{2}+{x}^{\mathrm{2}} }} \\ $$$${f}'\left({x}\right)=…??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:\mathrm{2}^{\frac{\mathrm{1}−{x}}{\mathrm{2}+{x}^{\mathrm{2}} }} \left(\mathrm{ln}\:\mathrm{2}\right)\left[\frac{{x}^{\mathrm{2}}…