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Category: Algebra

In-ABC-then-cos-A-2-cos-B-2-cos-C-2-1-sin-A-2-1-sin-B-2-1-sin-C-2-3-3-

Question Number 170115 by Shrinava last updated on 16/May/22 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{cos}\:\frac{\mathrm{A}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{B}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{C}}{\mathrm{2}}}{\left(\mathrm{1}\:-\:\mathrm{sin}\:\frac{\mathrm{A}}{\mathrm{2}}\right)\centerdot\left(\mathrm{1}\:-\:\mathrm{sin}\:\frac{\mathrm{B}}{\mathrm{2}}\right)\centerdot\left(\mathrm{1}\:-\:\mathrm{sin}\:\frac{\mathrm{C}}{\mathrm{2}}\right)}\:\geqslant\:\mathrm{3}\sqrt{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-170100

Question Number 170100 by mathlove last updated on 16/May/22 Commented by cortano1 last updated on 16/May/22 $$\:{y}=−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:{x}−\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{cos}\:{x} \\ $$$${y}=−\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:{x}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:{x}\right) \\ $$$${y}=−\left(\mathrm{sin}\:\frac{\pi}{\mathrm{6}}\:\mathrm{cos}\:{x}\:+\:\mathrm{cos}\:\frac{\pi}{\mathrm{6}}\:\mathrm{sin}\:{x}\right) \\ $$$${y}=−\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{6}}\right) \\ $$…

let-p-x-1-e-i-x-n-1-e-i-x-n-with-n-integr-natural-1-find-the-roots-of-p-x-2-fctorize-inside-C-x-p-x-3-factorize-inside-R-x-p-x-R-

Question Number 39022 by maxmathsup by imad last updated on 01/Jul/18 $${let}\:{p}\left({x}\right)=\:\left(\mathrm{1}+{e}^{{i}\theta} {x}\right)^{{n}} \:−\left(\mathrm{1}−{e}^{{i}\theta} {x}\right)^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{fctorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{inside}\:{R}\left[{x}\right]\:{p}\left({x}\right).\:\:\theta\:\in{R} \\ $$ Commented…

a-2-2-b-3-3-c-4-4-and-a-b-c-192-faind-a-b-c-

Question Number 170064 by mathlove last updated on 15/May/22 $$\frac{\left({a}−\mathrm{2}\right)}{\mathrm{2}}=\frac{\left({b}−\mathrm{3}\right)}{\mathrm{3}}=\frac{\left({c}−\mathrm{4}\right)}{\mathrm{4}} \\ $$$${and}\:\:\:\:{a}\centerdot{b}\centerdot{c}=\mathrm{192} \\ $$$${faind}\:\:\:{a}+{b}+{c}=? \\ $$ Answered by Rasheed.Sindhi last updated on 15/May/22 $$\frac{\left({a}−\mathrm{2}\right)}{\mathrm{2}}=\frac{\left({b}−\mathrm{3}\right)}{\mathrm{3}}=\frac{\left({c}−\mathrm{4}\right)}{\mathrm{4}} \\…