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Category: Trigonometry

Question-200785

Question Number 200785 by cortano12 last updated on 23/Nov/23 Answered by som(math1967) last updated on 24/Nov/23 $$\:\frac{{AB}}{{sin}\mathrm{105}}=\frac{{AT}}{{sin}\mathrm{45}} \\ $$$$\Rightarrow{AB}=\mathrm{24}×{sin}\mathrm{75}×\sqrt{\mathrm{2}} \\ $$$$\:\measuredangle{ATC}=\measuredangle{ACT}=\mathrm{75} \\ $$$$\therefore{AT}={AC}=\mathrm{24}{cm} \\ $$$$\bigtriangleup{ABC}=\frac{\mathrm{1}}{\mathrm{2}}×{AB}×{AC}×{sin}\mathrm{60}…

Question-200646

Question Number 200646 by Calculusboy last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\left(\frac{\mathrm{1}+\mathrm{sin}\:\theta\:+\mathrm{i}\:\mathrm{cos}\:\theta}{\mathrm{1}+\mathrm{sin}\:\theta\:−\mathrm{i}\:\mathrm{cos}\:\theta}\right)^{{n}} =\left(\mathrm{sin}\:\theta\:+\mathrm{i}\:\mathrm{cos}\:\theta\right)^{{n}} = \\ $$$$=\left(\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}−\theta\right)\:+\mathrm{i}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\theta\right)\right)^{{n}} =\mathrm{e}^{\mathrm{i}\left(\frac{\pi}{\mathrm{2}}−\theta\right){n}} = \\ $$$$=\mathrm{cos}\:\left(\left(\frac{\pi}{\mathrm{2}}−\theta\right){n}\right)\:+\mathrm{i}\:\mathrm{sin}\:\left(\left(\frac{\pi}{\mathrm{2}}−\theta\right){n}\right)…

Question-200379

Question Number 200379 by cortano12 last updated on 18/Nov/23 Commented by Frix last updated on 18/Nov/23 $$\mathrm{No}\:\mathrm{exact}\:\mathrm{solutions}\:\mathrm{possible}.\:\mathrm{Transform}\:\mathrm{to} \\ $$$$\begin{cases}{{y}^{\mathrm{2}} +\frac{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{\mathrm{2}\left({x}+\mathrm{1}\right)}{y}+\frac{{x}^{\mathrm{2}} +{x}−\mathrm{20}}{\mathrm{4}\left({x}+\mathrm{1}\right)}=\mathrm{0}}\\{{y}^{\mathrm{2}} +\frac{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{6}}{\mathrm{2}{x}\left({x}+\mathrm{1}\right)}{y}+\frac{\mathrm{3}{x}−\mathrm{20}}{\mathrm{2}{x}\left({x}+\mathrm{1}\right)}=\mathrm{0}}\end{cases} \\…

Question-199952

Question Number 199952 by Abdullahrussell last updated on 11/Nov/23 Answered by cortano12 last updated on 11/Nov/23 $$\:=\:\frac{\mathrm{2sin}\:\mathrm{7}\theta\:\mathrm{cos}\:\mathrm{2}\theta\:+\:\mathrm{2sin}\:\mathrm{7}\theta\:\mathrm{cos}\:\mathrm{6}\theta}{\mathrm{2cos}\:\mathrm{7}\theta\:\mathrm{cos}\:\mathrm{2}\theta\:+\:\mathrm{2cos}\:\mathrm{7}\theta\:\mathrm{cos}\:\mathrm{6}\theta} \\ $$$$\:=\:\frac{\mathrm{sin}\:\mathrm{7}\theta\left(\mathrm{cos}\:\mathrm{2}\theta+\mathrm{cos}\:\mathrm{6}\theta\right)}{\mathrm{cos}\:\mathrm{7}\theta\left(\mathrm{cos}\:\mathrm{2}\theta+\mathrm{cos}\:\mathrm{6}\theta\right)} \\ $$$$\:=\:\mathrm{tan}\:\mathrm{7}\theta \\ $$ Terms of…

Si-cos-x-sin-x-1-3-2-halle-el-valor-de-la-expresion-R-16-sin-6-x-cos-6-x-3-sec-2-x-csc-2-x-

Question Number 199830 by cortano12 last updated on 10/Nov/23 $$\:\:\mathrm{Si}\:\mathrm{cos}\:\mathrm{x}+\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\mathrm{2}}\:, \\ $$$$\:\mathrm{halle}\:\mathrm{el}\:\mathrm{valor}\:\mathrm{de}\:\mathrm{la}\:\mathrm{expresion}\: \\ $$$$\:\mathrm{R}=\:\mathrm{16}\left(\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}\right)+\mathrm{3}\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{csc}^{\mathrm{2}} \:\mathrm{x}\right) \\ $$ Answered by Frix last updated…

ABFE-Care-determiner-x-en-fonction-de-a-etb-BC-a-DE-b-

Question Number 199821 by a.lgnaoui last updated on 09/Nov/23 $$\mathrm{ABFE}\:\:\mathrm{Care} \\ $$$$\mathrm{determiner}\:\boldsymbol{\mathrm{x}}\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\mathrm{a}\:\mathrm{etb} \\ $$$$\mathrm{BC}=\boldsymbol{\mathrm{a}}\:\:\:\:\:\:\mathrm{DE}=\:\boldsymbol{\mathrm{b}} \\ $$ Commented by a.lgnaoui last updated on 09/Nov/23 Commented by…