Question Number 114627 by john santu last updated on 20/Sep/20 $$\mathrm{sin}\:{A}+\mathrm{sin}\:\mathrm{2}{A}+\mathrm{sin}\:\mathrm{3}{A}+…+\mathrm{sin}\:{nA}\:=?? \\ $$ Answered by mathmax by abdo last updated on 20/Sep/20 $$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} \left(\mathrm{x}\right)\:=\mathrm{sinx}\:+\mathrm{sin}\left(\mathrm{2x}\right)+…+\mathrm{sin}\left(\mathrm{nx}\right)=\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}}…
Question Number 49064 by Rio Michael last updated on 02/Dec/18 $${solve}\:{for}\:\mathrm{0}°\leqslant\theta\leqslant\mathrm{2}\pi\:{the}\:{equation} \\ $$$${cos}\left(\theta\:+\:\frac{\pi}{\mathrm{3}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by hknkrc46 last updated on 02/Dec/18 $$\mathrm{cos}\:\left(\theta+\frac{\pi}{\mathrm{3}}\right)=\mathrm{cos}\:\left(\frac{\pi}{\mathrm{3}}\right) \\ $$$$\theta+\frac{\pi}{\mathrm{3}}=\frac{\pi}{\mathrm{3}}+\mathrm{2}\pi{k}\:\vee\:−\left(\theta+\frac{\pi}{\mathrm{3}}\right)=\frac{\pi}{\mathrm{3}}+\mathrm{2}\pi{k}\:\left({k}\in\mathbb{Z}\right)…
Question Number 180025 by cortano1 last updated on 06/Nov/22 $$\:\:\:\:\:\:\:\mathrm{4}−\mathrm{2cos}\:\left(\mathrm{2}\pi\left(\mathrm{13x}+\mathrm{9}\right)^{\mathrm{2}} \right)=\:\mathrm{5sin}\:\left(\pi\left(\mathrm{13x}+\mathrm{9}\right)^{\mathrm{2}} \right) \\ $$$$\:\mathrm{x}=? \\ $$ Answered by Frix last updated on 06/Nov/22 $$\mathrm{4}−\mathrm{2cos}\:\mathrm{2}\alpha\:=\mathrm{5sin}\:\alpha \\…
Question Number 180018 by cortano1 last updated on 06/Nov/22 $$\:\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)}{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)}\:+\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)}{\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)}\:+\mathrm{1}−\mathrm{2sin}\:\left(\frac{\mathrm{5}\pi}{\mathrm{14}}\right)\:=? \\ $$ Commented by Frix last updated on 06/Nov/22 $$\mathrm{2} \\ $$ Terms…
Question Number 114409 by bemath last updated on 19/Sep/20 $${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 $${cosx}\:=\:{cos}\left(\mathrm{60}°\:−\:\mathrm{30}°\right) \\ $$$${cosx}\:=\:{cos}\left(\mathrm{30}°\right) \\ $$$${x}\:=\:\mathrm{30}° \\ $$…