Question Number 112542 by bobhans last updated on 08/Sep/20 $$\mathrm{If}\:\mathrm{7}\:\mathrm{sin}\:\mathrm{y}\:=\:\mathrm{8}\:\mathrm{sin}\:\left(\mathrm{y}+\mathrm{45}°\right).\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\left(\mathrm{y}+\mathrm{45}°\right)\:? \\ $$ Answered by bemath last updated on 08/Sep/20 $$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{y}+\mathrm{45}°\:;\:\mathrm{y}\:=\:\mathrm{x}−\mathrm{45}° \\ $$$$\Leftrightarrow\:\mathrm{7}\:\mathrm{sin}\:\left(\mathrm{x}−\mathrm{45}°\right)\:=\:\mathrm{8}\:\mathrm{sin}\:\mathrm{x} \\ $$$$\Leftrightarrow\:\mathrm{7}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}.\mathrm{sin}\:\mathrm{x}−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}.\mathrm{cos}\:\mathrm{x}\right)\:=\:\mathrm{8sin}\:\mathrm{x} \\…
Question Number 46944 by Tawa1 last updated on 02/Nov/18 Commented by maxmathsup by imad last updated on 03/Nov/18 $${we}\:{have}\:\frac{{x}}{{y}}\:+\frac{{y}}{{x}}\:=\frac{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{{xy}}\:\:{and} \\ $$$$\frac{{x}}{{sin}\theta}\:=\frac{{y}}{{cos}\theta}\:\Rightarrow\frac{{x}^{\mathrm{4}} }{{sin}^{\mathrm{4}} \theta}\:=\frac{{y}^{\mathrm{4}}…
Question Number 112466 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by 1549442205PVT last updated on 08/Sep/20 $$\mid\mathrm{cosx}\mid\geqslant\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \mathrm{x}\Leftrightarrow\mid\mathrm{cosx}\mid\geqslant\mathrm{cos}^{\mathrm{2}} \mathrm{x}=\mid\mathrm{cosx}\mid^{\mathrm{2}} \\ $$$$\Leftrightarrow\mid\mathrm{cosx}\mid\leqslant\mathrm{1}.\mathrm{The}\:\mathrm{last}\:\mathrm{inequality}\:\mathrm{is}\: \\ $$$$\mathrm{always}\:\mathrm{true}\:\forall\mathrm{x}.\mathrm{Hence},\mid\mathrm{cosx}\mid\geqslant\mathrm{1}−\mathrm{sin}^{\mathrm{2}}…
Question Number 177964 by mathlove last updated on 11/Oct/22 $$\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$ Commented by cortano1 last updated on 11/Oct/22 $$\:\frac{\mathrm{cos}\:\mathrm{15}°}{\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{15}°}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}\:\mathrm{cot}\:\mathrm{15}°=\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}×\left(\mathrm{2}+\sqrt{\mathrm{3}}\right) \\ $$$$=\:\frac{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{3}}}\:=\mathrm{2}+\frac{\mathrm{4}\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$$\left(\bullet\right)\:\mathrm{tan}\:\mathrm{15}°=\frac{\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}}{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}} \\…
Question Number 177914 by mathlove last updated on 11/Oct/22 $$\left(\mathrm{1}\right)\:\:\:\:\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{4}{sin}\mathrm{13}\:{cos}\mathrm{13}}=? \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 11/Oct/22 $$\left(\mathrm{1}\right)\:\:\:\:\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{4}{sin}\mathrm{13}\:{cos}\mathrm{13}}=? \\ $$$$\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{2}{sin}\mathrm{26}\:}−\mathrm{1}+\mathrm{1} \\…
Question Number 177793 by cortano1 last updated on 09/Oct/22 $$\:\:\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\:\:\frac{\mathrm{sec}\:^{\mathrm{4}} \alpha}{\mathrm{tan}\:^{\mathrm{2}} \beta}\:+\:\frac{\mathrm{sec}\:^{\mathrm{4}} \beta}{\mathrm{tan}\:^{\mathrm{2}} \alpha}\: \\ $$$$\:\:\mathrm{over}\:\mathrm{all}\:\alpha,\beta\:\neq\:\frac{\mathrm{k}\pi}{\mathrm{2}}\:,\:\mathrm{k}\:\varepsilon\:\mathbb{Z}\: \\ $$ Answered by mahdipoor last updated…
Question Number 177792 by cortano1 last updated on 09/Oct/22 $$\:\:\mathrm{Let}\:\mathrm{f}_{\mathrm{k}} \left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{k}}\left(\mathrm{sin}\:^{\mathrm{k}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{k}} \left(\mathrm{x}\right)\right) \\ $$$$\:\:\mathrm{for}\:\mathrm{k}=\mathrm{1},\mathrm{2},\mathrm{3},…\:.\: \\ $$$$\:\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\mathrm{f}_{\mathrm{4}} \left(\mathrm{x}\right)−\mathrm{f}_{\mathrm{6}} \left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{12}}\:\mathrm{for}\:\mathrm{all}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{x} \\ $$ Answered by…
Question Number 177791 by cortano1 last updated on 09/Oct/22 $$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}−\mathrm{cot}\:\mathrm{23}°\:=\:\frac{\mathrm{2}}{\mathrm{1}−\mathrm{cot}\:\mathrm{22}°}\: \\ $$ Answered by som(math1967) last updated on 09/Oct/22 $${cot}\mathrm{45}=\mathrm{1} \\ $$$$\:{cot}\left(\mathrm{23}+\mathrm{22}\right)=\mathrm{1} \\…
Question Number 112254 by john santu last updated on 07/Sep/20 $$\:\:\:\mathrm{sin}\:\left(\frac{\pi}{\:\mathrm{7}}\right).\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right).\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=? \\ $$ Answered by bemath last updated on 07/Sep/20 Terms of Service Privacy Policy…
Question Number 112173 by bobhans last updated on 06/Sep/20 $$\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation}\: \\ $$$$\sqrt{\mathrm{cos}\:\mathrm{2x}−\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{3}}\:=\:\mathrm{sin}\:\mathrm{x}\: \\ $$ Answered by john santu last updated on 06/Sep/20 $${since}\:\mathrm{sin}\:{x}\:\geqslant\:\mathrm{0}\:,\:{then}\: \\…