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Category: Trigonometry

if-sin-x-3-cos-x-1-2-3-sin-4x-cos-4x-

Question Number 191344 by mnjuly1970 last updated on 23/Apr/23 $$ \\ $$$$\:\:\:\:\:\:\mathrm{if}\:\:\:{sin}\left({x}\right)\:+\:\sqrt{\mathrm{3}}\:{cos}\:\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\sqrt{\mathrm{3}}\:\:{sin}\left(\mathrm{4}{x}\:\right)\:−\:\:{cos}\:\left(\mathrm{4}{x}\:\right)=\:? \\ $$$$ \\ $$ Answered by mehdee42 last updated on 23/Apr/23…

Question-191323

Question Number 191323 by Mingma last updated on 23/Apr/23 Answered by mr W last updated on 23/Apr/23 $$\frac{{A}}{{A}+{B}}=\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\frac{{A}}{{A}+{B}+{C}}=\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\Rightarrow{A}=\frac{{A}+{B}+{C}}{\mathrm{9}} \\…

Question-191278

Question Number 191278 by Mingma last updated on 22/Apr/23 Answered by a.lgnaoui last updated on 23/Apr/23 $$\mathrm{chaque}\:\mathrm{heptagone}\:\mathrm{a}\:\mathrm{7}\:\mathrm{triangles}\:\mathrm{isoceles}\:\mathrm{de}\:\mathrm{somet}\:\mathrm{O} \\ $$$$\mathrm{d}\:\mathrm{angle}\:\boldsymbol{\theta}=\frac{\mathrm{2}\pi}{\mathrm{7}}\:\:\mathrm{de}\:\mathrm{cote}\:\boldsymbol{\mathrm{x}}\:\:\mathrm{avec}\:\:\:\:\boldsymbol{\mathrm{x}}\mathrm{sin}\:\frac{\boldsymbol{\theta}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{xsin}\:\frac{\pi}{\mathrm{7}}=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\mathrm{x}=\frac{\mathrm{1}}{\mathrm{2sin}\:\frac{\pi}{\mathrm{7}}} \\ $$$$\:\mathrm{du}\:\mathrm{rayon}\:\mathrm{du}\:\mathrm{cercle}\:\mathrm{circonscrit}\:\boldsymbol{\mathrm{r}}=\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{s}}=\boldsymbol{\mathrm{y}}.\boldsymbol{\mathrm{x}}\:\:\:;\:\:\:\:\:\:\:\:\left[\:\boldsymbol{\mathrm{y}}^{\mathrm{2}}…