Menu Close

Author: Tinku Tara

Question-196251

Question Number 196251 by sonukgindia last updated on 20/Aug/23 Answered by MrGHK last updated on 20/Aug/23 $${x}+{y}=\frac{{ln}\left(\mathrm{3}\right)}{{ln}\left(\mathrm{2}\right)} \\ $$$${x}−{y}=\frac{\mathrm{2}{ln}\left(\mathrm{2}\right)}{{ln}\left(\mathrm{3}\right)} \\ $$$$\left({x}+{y}\right)\left({x}−{y}\right)=\frac{{ln}\left(\mathrm{3}\right)}{{ln}\left(\mathrm{2}\right)}×\frac{\mathrm{2}{ln}\left(\mathrm{2}\right)}{{ln}\left(\mathrm{3}\right)} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{2}…

Show-that-cos-pi-3-i-1-4-e-1-e-3-4-e-1-e-i-

Question Number 196211 by pete last updated on 20/Aug/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{cos}\left(\frac{\pi}{\mathrm{3}}+\mathrm{i}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{e}+\frac{\mathrm{1}}{\mathrm{e}}\right)\:−\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\left(\mathrm{e}−\frac{\mathrm{1}}{\mathrm{e}}\right)\mathrm{i} \\ $$ Answered by Frix last updated on 20/Aug/23 $$\mathrm{cos}\:{x}\:=\frac{\mathrm{e}^{\mathrm{2i}{x}} +\mathrm{1}}{\mathrm{2e}^{\mathrm{i}{x}} } \\ $$$$\mathrm{cos}\:\left({a}+{b}\mathrm{i}\right)\:=\mathrm{cos}\:{a}\:\mathrm{cosh}\:{b}\:−\mathrm{i}\:\mathrm{sin}\:{a}\:\mathrm{sinh}\:{b} \\…

Simplify-1-cos2-isin2-1-cos2-isin2-30-

Question Number 196242 by pete last updated on 20/Aug/23 $$\mathrm{Simplify}\:\left(\frac{\mathrm{1}+\mathrm{cos2}\theta\:+\mathrm{isin2}\theta}{\mathrm{1}+\mathrm{cos2}\theta\:−\mathrm{isin2}\theta}\right)^{\mathrm{30}} \\ $$ Answered by MM42 last updated on 20/Aug/23 $$\left(\frac{\mathrm{2}{cos}^{\mathrm{2}} \theta+\mathrm{2}{isin}\theta{cos}\theta}{\mathrm{2}{cos}^{\mathrm{2}} \theta−\mathrm{2}{isin}\theta{cos}\theta}\right)^{\mathrm{30}} =\left(\frac{{cos}\theta+{isin}\theta}{{cos}\theta−{isin}\theta}\right)^{\mathrm{30}} \\ $$$$={cos}\left(\mathrm{60}\theta\right)+{isin}\left(\mathrm{60}\theta\right)\:\checkmark…

Question-196185

Question Number 196185 by cortano12 last updated on 19/Aug/23 $$\:\:\:\underbrace{\:} \\ $$ Commented by AST last updated on 19/Aug/23 $${When}\:{x}={y}={z}\:\wedge\:{a}={b}={c};\frac{{ab}+{bc}+{ca}}{{bc}}=\mathrm{3} \\ $$$${When}\:{x}=−\mathrm{1},{y}=\mathrm{1},{z}=\mathrm{1};\:\frac{{ab}+{bc}+{ca}}{{bc}}=\frac{{a}\left({b}+{c}\right)}{{bc}}+\mathrm{1} \\ $$$${can}\:{get}\:{multiple}\:{values}\:{since}\:{a},{b},{c}\:{can}\:{vary}. \\…

Question-196154

Question Number 196154 by sonukgindia last updated on 19/Aug/23 Answered by mr W last updated on 19/Aug/23 $${x}^{\mathrm{2}} =−\mathrm{2}\left({x}+\mathrm{2}\right) \\ $$$${x}^{\mathrm{4}} =\mathrm{4}\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{4}\right)=\mathrm{4}\left(\mathrm{2}{x}\right)=\mathrm{8}{x} \\ $$$${x}^{\mathrm{6}}…