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Author: Tinku Tara

Question-226194

Question Number 226194 by fantastic2 last updated on 22/Nov/25 Answered by gregori last updated on 22/Nov/25 $$\:\:\measuredangle\: =\:\mathrm{60}°\: \\ $$$$\:\:\measuredangle\: =\:\mathrm{60}°\: \\ $$$$\:\:\measuredangle\: =\:\mathrm{360}°−\left(\mathrm{2}×\mathrm{120}°+\mathrm{60}°\right)\:=\:\mathrm{60}°\: \\…

Question-226178

Question Number 226178 by Spillover last updated on 22/Nov/25 Answered by mr W last updated on 22/Nov/25 $$=\int\frac{\mathrm{1}+\frac{\mathrm{1}}{{x}}}{{x}+\frac{\mathrm{1}}{{x}}}{dx} \\ $$$$=\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{d}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}+\int\frac{\mathrm{1}}{{x}^{\mathrm{2}}…

Q226015-

Question Number 226134 by fantastic2 last updated on 20/Nov/25 $${Q}\mathrm{226015} \\ $$ Answered by fantastic2 last updated on 20/Nov/25 $${f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)={x}\:…{i} \\ $$$${put}\:{x}=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}}\right)=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\…