Question Number 114409 by bemath last updated on 19/Sep/20 $${find}\:{solution}\:{set}\:{of}\:{equation} \\ $$$$\:\mathrm{sin}\:{x}\:=\:\mathrm{2}\:,\:{x}\:\in\:\mathbb{C}\:. \\ $$ Answered by bobhans last updated on 19/Sep/20 $$\mathrm{sin}\:{x}\:=\:\frac{{e}^{{ix}} −{e}^{−{ix}} }{\mathrm{2}{i}}\:=\:\mathrm{2}\: \\…
Question Number 48851 by vajpaithegrate@gmail.com last updated on 29/Nov/18 $$\mathrm{the}\:\mathrm{total}\:\mathrm{no}\:\mathrm{of}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{sin}\left\{\mathrm{x}\right\}=\mathrm{cos}\left\{\mathrm{x}\right\} \\ $$$$\mathrm{where}\left\{\mathrm{x}\right\}\:\mathrm{denotes}\:\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:\mathrm{x}\:\mathrm{in} \\ $$$$\left[\mathrm{o}\:\mathrm{2}\pi\right]\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\mathrm{ans}:\mathrm{6} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18…
Question Number 48852 by vajpaithegrate@gmail.com last updated on 29/Nov/18 $$\mathrm{A}\:\mathrm{polygon}\:\mathrm{of}\:\mathrm{nine}\:\mathrm{sides}\:\mathrm{each}\:\mathrm{of}\:\mathrm{length}\:\mathrm{2} \\ $$$$\mathrm{is}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle},\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{circle} \\ $$$$\mathrm{ans}:\mathrm{cosec}\:\mathrm{20} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18…
Question Number 179917 by mnjuly1970 last updated on 04/Nov/22 Answered by a.lgnaoui last updated on 06/Nov/22 $$\:\:\:\frac{\mathrm{1}}{\mathrm{4}^{{n}} \mathrm{cos}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}^{{n}+\mathrm{2}} }\right)}=\frac{\mathrm{1}}{\mathrm{4}^{{n}} }\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}^{{n}+\mathrm{2}} }\right)\right. \\ $$$$\mathrm{tan}\:\left({x}\right)\cong{x}+\frac{{x}^{\mathrm{3}}…
Question Number 48849 by vajpaithegrate@gmail.com last updated on 29/Nov/18 $$\mathrm{in}\:\left(\mathrm{0}\:\pi\right)\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{tan}\theta+\mathrm{tan2}\theta+\mathrm{tan3}\theta=\mathrm{tan}\theta\mathrm{tan2}\theta\mathrm{tan3}\theta \\ $$$$\mathrm{is} \\ $$$$\mathrm{ans}:\mathrm{2} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18…
Question Number 48769 by somil last updated on 28/Nov/18 Answered by Abdulhafeez Abu qatada last updated on 28/Nov/18 $${cosx}\:=\:{cos}\left(\mathrm{60}°\:−\:\mathrm{30}°\right) \\ $$$${cosx}\:=\:{cos}\left(\mathrm{30}°\right) \\ $$$${x}\:=\:\mathrm{30}° \\ $$…
Question Number 114272 by bemath last updated on 18/Sep/20 $${find}\:{solution}\:{set}\:{of}\:{equation}\: \\ $$$$\mathrm{cos}\:\mathrm{3}{x}\:=\:−\mathrm{cos}\:{x}\:,\:{x}\in\left(\mathrm{0},\mathrm{3}\pi\right) \\ $$ Commented by malwaan last updated on 18/Sep/20 $$\left({i}\right)\:{cos}\:\mathrm{3}{x}=\:{cos}\:\left(\pi−{x}\right) \\ $$$$\Rightarrow\mathrm{3}{x}=\:\pm\left(\pi−{x}\right)+\mathrm{2}{k}\pi \\…
Question Number 48711 by somil last updated on 27/Nov/18 Commented by mr W last updated on 27/Nov/18 $${A}+{B}+{C}=\pi \\ $$$${A}+{B}=\pi−{C} \\ $$$$\frac{{A}+{B}}{\mathrm{2}}=\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\left(\frac{{A}+{B}}{\mathrm{2}}\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}}\right)=\mathrm{cos}\:\frac{{C}}{\mathrm{2}} \\…
Question Number 114122 by bemath last updated on 17/Sep/20 $${find}\:{the}\:{value}\:\mathrm{sin}\:\left(\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{5}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{7}}{\mathrm{13}}\right)\right) \\ $$ Answered by mr W last updated on 17/Sep/20 $$\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{7}}{\mathrm{13}}=\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{7}}{\:\sqrt{\mathrm{218}}}=\mathrm{cos}^{−\mathrm{1}}…
Question Number 114108 by bemath last updated on 17/Sep/20 $${prove}\:{that}\:\mathrm{2}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{12}}{\mathrm{13}}\right) \\ $$ Answered by bobhans last updated on 17/Sep/20 $${let}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)\:=\:{x}\:\rightarrow\:\mathrm{tan}\:{x}\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${and}\:\begin{cases}{\mathrm{sin}\:{x}=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{13}}}}\\{\mathrm{cos}\:{x}\:=\:\frac{\mathrm{3}}{\:\sqrt{\mathrm{13}}}}\end{cases}…