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Question-129244

Question Number 129244 by ajfour last updated on 14/Jan/21 Commented by ajfour last updated on 14/Jan/21 $${In}\:{terms}\:{of}\:{the}\:{sides}\:{of}\:\bigtriangleup{ABC}, \\ $$$${find}\:{largest}\:{radius}\:{sphere}\:{that} \\ $$$${can}\:{be}\:{placed}\:{against}\:{the}\:{room} \\ $$$${corner}\:{and}\:{triangle}.\:\:\:\:\: \\ $$…

sin-3-x-cos-3-x-1-1-2-sin2x-x-0-2pi-find-x-

Question Number 63703 by kaivan.ahmadi last updated on 07/Jul/19 $${sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}{sin}\mathrm{2}{x}\:\::{x}\in\left[\mathrm{0},\mathrm{2}\pi\right]. \\ $$$${find}\:\:{x} \\ $$ Commented by Prithwish sen last updated on 08/Jul/19 $$\left(\mathrm{sinx}\:+\:\mathrm{cosx}\:\right)\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin2x}\right)\:−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin2x}\right)=\mathrm{0}…

cos-2-47-cos-2-73-cos-47-cos-73-1-2-

Question Number 129234 by bemath last updated on 14/Jan/21 $$\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{47}°+\mathrm{cos}^{\mathrm{2}} \:\:\mathrm{73}°+\mathrm{cos}\:\mathrm{47}°\mathrm{cos}\:\mathrm{73}°+\frac{\mathrm{1}}{\mathrm{2}}=? \\ $$ Answered by liberty last updated on 14/Jan/21 $$\left(\mathrm{cos}\:\mathrm{73}°+\mathrm{cos}\:\mathrm{47}°\right)^{\mathrm{2}} −\mathrm{cos}\:\mathrm{73}°\mathrm{cos}\:\mathrm{47}°+\frac{\mathrm{1}}{\mathrm{2}}= \\ $$$$\left(\mathrm{2cos}\:\mathrm{60}°\mathrm{cos}\:\mathrm{13}°\right)^{\mathrm{2}}…