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Author: Tinku Tara

sin-3-x-cos-3-x-sin-x-cos-x-1-Find-x-

Question Number 128743 by bemath last updated on 10/Jan/21 $$\:\:\:\:\:\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}\:+\:\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:+\:\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:=\:\mathrm{1} \\ $$$$\:\:\:\mathrm{Find}\:\mathrm{x}\:. \\ $$ Answered by liberty last updated on 10/Jan/21 $$\:\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{3}}…

n-0-1-n-1-n-3-n-

Question Number 128740 by bemath last updated on 10/Jan/21 $$\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{3}\right)\mathrm{n}!}\:=?\: \\ $$ Answered by liberty last updated on 10/Jan/21 $$\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{n}+\mathrm{2}}{\left(\mathrm{n}+\mathrm{3}\right)\left(\mathrm{n}+\mathrm{2}\right)\left(\mathrm{n}+\mathrm{1}\right)\mathrm{n}!}\:=\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty}…

Question-63194

Question Number 63194 by lalitchand last updated on 30/Jun/19 Answered by mr W last updated on 30/Jun/19 $$\frac{\Delta{AQR}}{\Delta{ABC}}=\left(\frac{{AQ}}{{AB}}\right)^{\mathrm{2}} =\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{4}}{\mathrm{9}} \\ $$$$\frac{\Delta{APS}}{\Delta{ABC}}=\left(\frac{{AP}}{{AB}}\right)^{\mathrm{2}} =\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{9}} \\…