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Author: Tinku Tara

Question-88261

Question Number 88261 by ar247 last updated on 09/Apr/20 Answered by Joel578 last updated on 09/Apr/20 $${u}\:\equiv\:{v}\:\left(\mathrm{mod}\:{m}\right)\:\Rightarrow\:{u}\:−\:{v}\:=\:{mx},\:{x}\:\in\:\mathbb{Z} \\ $$$$\left(\mathrm{1}\right)\:{u}\:=\:{mx}\:+\:{v} \\ $$$$\mathrm{Since}\:\mathrm{gcf}\left({v},{m}\right)\:\mathrm{divides}\:\mathrm{both}\:{v}\:\mathrm{and}\:\mathrm{m},\:\mathrm{it}\:\mathrm{also}\:\mathrm{divides}\:{u}, \\ $$$$\mathrm{hence}\:\mathrm{gcf}\left({v},{m}\right)\:\mathrm{divides}\:\mathrm{gcf}\left({u},{m}\right) \\ $$$$\Rightarrow\:\mathrm{gcf}\left({v},{m}\right)\:\mid\:\mathrm{gcf}\left({u},{m}\right)…

Question-22714

Question Number 22714 by selestian last updated on 22/Oct/17 Answered by ajfour last updated on 22/Oct/17 $$\lambda\:={a}+{b}+{c}\: \\ $$$${let}\:\:\:{l}={b}\mathrm{cos}\:^{\mathrm{2}} \left(\frac{{C}}{\mathrm{2}}\right)+{c}\mathrm{cos}\:^{\mathrm{2}} \left(\frac{{B}}{\mathrm{2}}\right) \\ $$$$\Rightarrow\:\:\:\:\mathrm{2}{l}={b}\left(\mathrm{1}+\mathrm{cos}\:{C}\right)+{c}\left(\mathrm{1}+\mathrm{cos}\:{B}\right) \\ $$$$\Rightarrow\:\:\:\:\mathrm{2}{l}={b}+{c}+\left({b}\mathrm{cos}\:{C}+{c}\mathrm{cos}\:{B}\right)…