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Author: Tinku Tara

4-sin-2-x-sin-2x-2-find-x-

Question Number 207561 by hardmath last updated on 18/May/24 $$\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{sin}\:\mathrm{2}\boldsymbol{\mathrm{x}}\:\:=\:\:\mathrm{2} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by mathzup last updated on 18/May/24 $${e}\Leftrightarrow\mathrm{4}\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}\:+{sin}\left(\mathrm{2}{x}\right)=\mathrm{2}\:\Leftrightarrow \\ $$$$\mathrm{2}−\mathrm{2}{cos}\left(\mathrm{2}{x}\right)+{sin}\left(\mathrm{2}{x}\right)=\mathrm{2}\:\Leftrightarrow…

z-z-1-3-i-find-

Question Number 207563 by hardmath last updated on 18/May/24 $$\mathrm{z}\:\:+\:\:\mid\mathrm{z}\mid\:\:=\:\:\mathrm{1}\:\:+\:\:\sqrt{\mathrm{3}}\:\boldsymbol{\mathrm{i}} \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\varphi}\:=\:? \\ $$ Answered by Frix last updated on 18/May/24 $${z}+\mid{z}\mid=\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i} \\ $$$$\mid{z}\mid=\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i}−{z} \\…

x-2-lg-x-3-0-

Question Number 207558 by hardmath last updated on 18/May/24 $$\left(\mathrm{x}\:−\:\mathrm{2}\right)\:\mathrm{lg}\:\frac{\mathrm{x}}{\mathrm{3}}\:\:\geqslant\:\:\mathrm{0} \\ $$ Answered by mr W last updated on 19/May/24 $${x}−\mathrm{2}\geqslant\mathrm{0}\:\wedge\:\frac{{x}}{\mathrm{3}}\geqslant\mathrm{1}\:\Rightarrow{x}\geqslant\mathrm{3}\:\checkmark \\ $$$${or} \\ $$$${x}−\mathrm{2}\leqslant\mathrm{0}\:\wedge\:\mathrm{0}<\frac{{x}}{\mathrm{3}}\leqslant\mathrm{1}\:\Rightarrow\mathrm{0}<{x}\leqslant\mathrm{2}\:\checkmark…

log-x-x-2-7-1-

Question Number 207559 by hardmath last updated on 18/May/24 $$\mathrm{log}_{\boldsymbol{\mathrm{x}}} \:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{7}\right)\:\:\leqslant\:\:\mathrm{1} \\ $$ Answered by mr W last updated on 19/May/24 $$\mathrm{log}_{{x}} \:\left({x}^{\mathrm{2}} +\mathrm{7}\right)−\mathrm{log}_{{x}}…

3-sin-cos-4-6-sin-cos-2-4-sin-6-cos-6-

Question Number 207516 by MATHEMATICSAM last updated on 17/May/24 $$\mathrm{3}\left(\mathrm{sin}\theta\:−\:\mathrm{cos}\theta\right)^{\mathrm{4}} \:+\:\mathrm{6}\left(\mathrm{sin}\theta\:+\:\mathrm{cos}\theta\right)^{\mathrm{2}} \\ $$$$+\:\mathrm{4}\left(\mathrm{sin}^{\mathrm{6}} \theta\:+\:\mathrm{cos}^{\mathrm{6}} \theta\right)\:=\:? \\ $$ Commented by A5T last updated on 17/May/24 $${Did}\:{you}\:{edit}\:{this}\:{question}\:{to}\:{change}\:{something}?…