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Author: Tinku Tara

x-3-7x-6-0-prove-that-x-2-3-1-

Question Number 75913 by ajfour last updated on 21/Dec/19 $${x}^{\mathrm{3}} −\mathrm{7}{x}+\mathrm{6}=\mathrm{0} \\ $$$${prove}\:{that}\:{x}=\mathrm{2},−\mathrm{3},\mathrm{1}\:. \\ $$ Commented by TawaTawa last updated on 21/Dec/19 $$\mathrm{Sir},\:\mathrm{please}\:\mathrm{solve}\:\mathrm{it},\:\mathrm{i}\:\mathrm{want}\:\mathrm{to}\:\mathrm{learn}\:\mathrm{your}\:\mathrm{approach}. \\ $$…

lim-x-pi-4-x-pi-4-sin-3x-3-pi-4-2-1-sin2x-

Question Number 10374 by ridwan balatif last updated on 06/Feb/17 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{\left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)\mathrm{sin}\left(\mathrm{3x}−\mathrm{3}\frac{\pi}{\mathrm{4}}\right)}{\mathrm{2}\left(\mathrm{1}−\mathrm{sin2x}\right)}=…? \\ $$ Answered by mrW1 last updated on 06/Feb/17 $${let}\:{u}={x}−\frac{\pi}{\mathrm{4}} \\ $$$${with}\:{x}\rightarrow\frac{\pi}{\mathrm{4}},\:{u}\rightarrow\mathrm{0} \\…

Let-P-be-the-point-a-2-t-2-1-t-2-a-t-1-t-Find-the-locus-of-P-as-t-varies-

Question Number 141446 by ZiYangLee last updated on 19/May/21 $$\mathrm{Let}\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{point}\:\left(\frac{{a}}{\mathrm{2}}\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right),{a}\left({t}−\frac{\mathrm{1}}{{t}}\right)\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{P},\:\mathrm{as}\:{t}\:\mathrm{varies}. \\ $$ Answered by 1549442205PVT last updated on 19/May/21 $$\mathrm{Let}\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{point}\:\left(\frac{{a}}{\mathrm{2}}\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}}…

Question-75901

Question Number 75901 by Master last updated on 20/Dec/19 Answered by MJS last updated on 20/Dec/19 $$\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \:{x}}=\mathrm{4tan}\:\mathrm{2}{x} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}}=\mathrm{2tan}\:\mathrm{2}{x} \\ $$$${x}=\mathrm{arctan}\:{t} \\ $$$$\frac{{t}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{4}{t}}{\mathrm{1}−{t}^{\mathrm{2}}…