Question Number 75209 by vishalbhardwaj last updated on 08/Dec/19 Answered by Kunal12588 last updated on 08/Dec/19 $${x}+{y}+{z}={xyz} \\ $$$${let}\:{x}={tan}\:\alpha,{y}={tan}\:\beta,\:{z}={tan}\:\gamma \\ $$$${tan}\:\alpha\:+\:{tan}\:\beta\:+\:{tan}\:\gamma\:=\:{tan}\:\alpha\:{tan}\:\beta\:{tan}\:\gamma \\ $$$$\Rightarrow{tan}\:\gamma\:\left(\mathrm{1}−{tan}\:\alpha\:{tan}\:\beta\right)=−\left({tan}\:\alpha+{tan}\:\beta\right) \\ $$$$\Rightarrow{tan}\:\gamma=−\frac{{tan}\:\alpha+{tan}\beta}{\mathrm{1}−{tan}\:\alpha\:{tan}\:\beta}=−{tan}\:\left(\alpha+\beta\right)…
Question Number 75147 by mathocean1 last updated on 07/Dec/19 $$\mathrm{hello} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\frac{\mathrm{5}\pi}{\mathrm{18}}\mathrm{cos}\frac{\mathrm{13}\pi}{\mathrm{18}}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\frac{\mathrm{4}\pi}{\mathrm{9}} \\ $$ Answered by MJS last updated on 07/Dec/19 $$\mathrm{sin}\:{a}\:\mathrm{cos}\:{b}\:=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{sin}\:\left({a}−{b}\right)\:+\mathrm{sin}\:\left({a}+{b}\right)\right) \\…
Question Number 9594 by tawakalitu last updated on 19/Dec/16 Answered by sandy_suhendra last updated on 20/Dec/16 Commented by tawakalitu last updated on 20/Dec/16 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\…
Question Number 75131 by mathocean1 last updated on 07/Dec/19 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{8}}\right)+\mathrm{2tan}\left(\frac{\pi}{\mathrm{8}}\right)−\mathrm{1}=\mathrm{0} \\ $$ Answered by mr W last updated on 07/Dec/19 $$\mathrm{tan}\:\frac{\pi}{\mathrm{4}}=\mathrm{1} \\…
Question Number 9589 by tawakalitu last updated on 19/Dec/16 Answered by ridwan balatif last updated on 19/Dec/16 Commented by tawakalitu last updated on 19/Dec/16 $$\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}.…
Question Number 140659 by bemath last updated on 11/May/21 $$\mathrm{Eliminate}\:\theta\:\mathrm{from}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\begin{cases}{\frac{\mathrm{x}}{\mathrm{a}}\mathrm{cos}\:\theta−\frac{\mathrm{y}}{\mathrm{b}}\mathrm{sin}\:\theta=\mathrm{cos}\:\mathrm{2}\theta}\\{\frac{\mathrm{x}}{\mathrm{a}}\mathrm{sin}\:\theta+\frac{\mathrm{y}}{\mathrm{b}}\mathrm{cos}\:\theta=\mathrm{2sin}\:\mathrm{2}\theta}\end{cases} \\ $$ Answered by BHOOPENDRA last updated on 11/May/21 Answered by BHOOPENDRA last…
Question Number 9525 by Joel575 last updated on 12/Dec/16 $$\mathrm{If}\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} ,\:…,\:{x}_{\mathrm{2009}\:} \in\:\mathbb{R} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{from} \\ $$$$\left(\mathrm{cos}\:{x}_{\mathrm{1}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{2}} \right)\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{3}} \right)\:+\:…\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2008}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{2009}} \right)\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2009}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{1}}…
Question Number 9515 by Joel575 last updated on 12/Dec/16 $$\mathrm{cos}\:\left({x}+\mathrm{2}{y}\right)\:=\:{a} \\ $$$$\mathrm{cos}\:\left({x}+{y}\right)\:=\:{b} \\ $$$$ \\ $$$$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{sin}^{\mathrm{2}} \:\left(\mathrm{2}{x}+\mathrm{3}{y}\right)\:\:\mathrm{is}\:… \\ $$ Answered by mrW last updated on…
Question Number 75048 by mathocean1 last updated on 06/Dec/19 $$\mathrm{I}\:\mathrm{would}\:\mathrm{like}\:\mathrm{that}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{show}\:\mathrm{this}\:\mathrm{equality}: \\ $$$$\mathrm{16cos}\:\frac{\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{5}\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{7}\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{11}\Pi}{\mathrm{24}}=\mathrm{1} \\ $$ Commented by mind is power last updated on 06/Dec/19…
Question Number 75040 by mathocean1 last updated on 06/Dec/19 $$\mathrm{Please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{to}\:\mathrm{show}\:\mathrm{that}: \\ $$$$\mathrm{cos}\:\frac{\mathrm{47}\Pi}{\mathrm{13}}=\mathrm{sin}\:\frac{\mathrm{23}\Pi}{\mathrm{26}}=\mathrm{sin}\frac{\mathrm{3}\Pi}{\mathrm{26}} \\ $$ Answered by Kunal12588 last updated on 06/Dec/19 $${cos}\frac{\mathrm{47}\pi}{\mathrm{13}}={cos}\left(\frac{\mathrm{52}\pi−\mathrm{5}\pi}{\mathrm{13}}\right)={cos}\left(\mathrm{4}\pi−\frac{\mathrm{5}\pi}{\mathrm{13}}\right) \\…