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 $${since}\:\mathrm{sin}\:{x}\:\geqslant\:\mathrm{0}\:,\:{then}\: \\…
Question Number 46637 by rahul 19 last updated on 29/Oct/18 Commented by tanmay.chaudhury50@gmail.com last updated on 29/Oct/18 $${ok}… \\ $$ Commented by rahul 19 last…
Question Number 46636 by azharkhan250963@gmail.com last updated on 29/Oct/18 $$\mathrm{tan}\:\theta=\mathrm{10tan60}^{°} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Oct/18 $${tan}\theta=\mathrm{10}×\sqrt{\mathrm{3}}\: \\ $$$${tan}\theta=\mathrm{10}×\mathrm{1}.\mathrm{732} \\ $$$$\theta={tan}^{−\mathrm{1}} \left(\mathrm{17}.\mathrm{32}\right)…
Question Number 177694 by cortano1 last updated on 08/Oct/22 Commented by Strengthenchen last updated on 08/Oct/22 $${as}\:{the}\:{picture}, \\ $$$$\frac{\mathrm{200}}{\mathrm{sin}\:{y}}=\frac{\mathrm{36}}{{sin}\:\mathrm{5}°}\rightarrow\mathrm{sin}\:{y}=\frac{\mathrm{sin}\:\mathrm{5}°×\mathrm{50}}{\mathrm{9}}\rightarrow\mathrm{cos}\:{y}=\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {y}} \\ $$$${x}^{\mathrm{2}} +\mathrm{36}^{\mathrm{2}} −\mathrm{72}{x}\mathrm{cos}\:{y}=\mathrm{200}^{\mathrm{2}} \rightarrow{x}=\frac{\mathrm{72cos}\:{y}\pm\sqrt{\left(\mathrm{72cos}\:{y}\right)^{\mathrm{2}}…
Question Number 112136 by weltr last updated on 06/Sep/20 $${find}\:\:\:\frac{\mathrm{5}}{\mathrm{6}+\mathrm{7sin}\:\mathrm{2}\beta}\:,\:\:\:{if}\:\:\:\mathrm{tan}\:\beta\:\:=\:\:\mathrm{0}.\mathrm{2} \\ $$ Answered by bemath last updated on 06/Sep/20 $$\mathrm{tan}\:\beta\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:\rightarrow\begin{cases}{{if}\:\:\beta\:{in}\:{I}−\:{quadrant}\rightarrow\begin{cases}{\mathrm{sin}\:\beta=\frac{\mathrm{1}}{\:\sqrt{\mathrm{26}}}}\\{\mathrm{cos}\:\beta=\frac{\mathrm{5}}{\:\sqrt{\mathrm{26}}}}\end{cases}}\\{{if}\:\beta\:{in}\:{III}−{quadrant}\rightarrow\begin{cases}{\mathrm{sin}\:\beta=−\frac{\mathrm{1}}{\:\sqrt{\mathrm{26}}}}\\{\mathrm{cos}\:\beta=−\frac{\mathrm{5}}{\:\sqrt{\mathrm{26}}}}\end{cases}}\end{cases} \\ $$$$\Leftrightarrow\:\frac{\mathrm{5}}{\mathrm{6}+\mathrm{14sin}\:\beta\mathrm{cos}\:\beta}\:=\:\frac{\mathrm{5}}{\mathrm{6}+\mathrm{14}\left(\frac{\mathrm{5}}{\mathrm{26}}\right)} \\ $$$$=\:\frac{\mathrm{5}×\mathrm{26}}{\mathrm{6}×\mathrm{26}+\mathrm{70}}\:=\:\frac{\mathrm{65}}{\mathrm{78}+\mathrm{35}}\:=\:\frac{\mathrm{65}}{\mathrm{113}} \\…
Question Number 46573 by Rio Michael last updated on 28/Oct/18 $${Show}\:{that}\: \\ $$$${sin}\mathrm{2}{x}\:\equiv\frac{\mathrm{2}{tanx}}{\mathrm{1}+{tan}^{\mathrm{2}} {x}} \\ $$ Commented by peter frank last updated on 28/Oct/18 $$\mathrm{sin2x}=\frac{\mathrm{2sinxcosx}}{\mathrm{1}}…