Question Number 15384 by Tinkutara last updated on 10/Jun/17 $$\mathrm{If}\:\mathrm{a}\:\mathrm{flagstaff}\:\mathrm{subtends}\:\mathrm{equal}\:\mathrm{angles}\:\mathrm{at}\:\mathrm{4} \\ $$$$\mathrm{points}\:{A},\:{B},\:{C}\:\mathrm{and}\:{D}\:\mathrm{on}\:\mathrm{the}\:\mathrm{horizontal} \\ $$$$\mathrm{plane}\:\mathrm{through}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{flagstaff}, \\ $$$$\mathrm{then}\:{A},\:{B},\:{C}\:\mathrm{and}\:{D}\:\mathrm{must}\:\mathrm{be}\:\mathrm{the} \\ $$$$\mathrm{vertices}\:\mathrm{of} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Square} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Cyclic}\:\mathrm{quadrilateral} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Rectangle} \\…
Question Number 80896 by mathocean1 last updated on 07/Feb/20 $$\left.\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\in\:\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[.\:\mathrm{we}\:\mathrm{give}\:\mathrm{this}\:\right. \\ $$$$\left(\mathrm{E}_{\alpha} \right):\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}\sqrt{\mathrm{2}}\left({cos}\alpha\right)+\mathrm{cos2}\alpha=\mathrm{0} \\ $$$$\mathrm{1}.\:\mathrm{show}\:\mathrm{that}\:\Delta=\mathrm{8sin}^{\mathrm{2}} {x} \\ $$$${i}\:{showed}\:{it}. \\ $$$$\mathrm{2}.{S}\mathrm{olve}\:\mathrm{E}_{\alpha} \:\mathrm{in}\:\mathbb{R}. \\ $$$$ \\…
Question Number 146404 by iloveisrael last updated on 13/Jul/21 $$\:\mathrm{trigonometry} \\ $$ Commented by iloveisrael last updated on 13/Jul/21 Answered by gsk2684 last updated on…
Question Number 15328 by tawa tawa last updated on 09/Jun/17 $$\mathrm{Prove}\:\mathrm{that}. \\ $$$$\mathrm{sec}^{\mathrm{4}} \left(\mathrm{x}\right)\:−\:\mathrm{cosec}^{\mathrm{4}} \left(\mathrm{x}\right)\:=\:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\:−\:\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{sec}^{\mathrm{4}} \left(\mathrm{x}\right)} \\ $$ Answered by RasheedSoomro last updated…
Question Number 15300 by Tinkutara last updated on 09/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\alpha\:\mathrm{and}\:\beta,\:\mathrm{0}\:<\:\alpha,\:\beta\:<\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation} \\ $$$$\mathrm{cos}\:\alpha\:\mathrm{cos}\:\beta\:\mathrm{cos}\:\left(\alpha\:+\:\beta\right)\:=\:−\frac{\mathrm{1}}{\mathrm{8}}\:. \\ $$ Commented by mrW1 last updated on 09/Jun/17 $$\alpha=\beta=\frac{\pi}{\mathrm{3}} \\…
Question Number 15301 by Tinkutara last updated on 09/Jun/17 $$\mathrm{With}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{graph},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequation}\:\mathrm{tan}\:{x}\:>\:−\sqrt{\mathrm{3}}\:. \\ $$ Answered by mrW1 last updated on 09/Jun/17 $$\mathrm{x}\in\left(\mathrm{n}\pi−\frac{\pi}{\mathrm{3}},\:\mathrm{n}\pi+\frac{\pi}{\mathrm{2}}\right)\:\wedge\:\mathrm{n}\in\mathbb{Z} \\ $$ Commented…
Question Number 15298 by Tinkutara last updated on 09/Jun/17 $$\mathrm{Solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:\mathrm{sin}\left({xy}\right)\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$ Commented by prakash jain last updated on 10/Jun/17 $${xy}={u} \\…
Question Number 15267 by Tinkutara last updated on 09/Jun/17 $$\mathrm{In}\:\mathrm{an}\:\mathrm{acute}\:\mathrm{angled}\:\Delta{ABC},\:\mathrm{the} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:{A}\:\mathrm{tan}\:{B}\:\mathrm{tan}\:{C}\:\mathrm{is}? \\ $$ Commented by prakash jain last updated on 09/Jun/17 $${A}=\mathrm{0}.\mathrm{1}°,{B}=\mathrm{89}.\mathrm{5}°,{C}=\mathrm{89}.\mathrm{5}° \\ $$$$\mathrm{tan}\:{A}\mathrm{tan}\:{B}\mathrm{tan}\:{C}=.\mathrm{518}…
Question Number 15264 by Tinkutara last updated on 08/Jun/17 $$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequation} \\ $$$$\mathrm{cos}\:{x}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\geqslant\:\mathrm{0}\:\mathrm{is}\:\left[−\pi,\:\pi\right] \\ $$$$\left(\mathrm{1}\right)\:\left[\mathrm{0},\:\frac{\mathrm{2}\pi}{\mathrm{3}}\right] \\ $$$$\left(\mathrm{2}\right)\:\left[−\frac{\mathrm{2}\pi}{\mathrm{3}},\:\frac{\mathrm{2}\pi}{\mathrm{3}}\right] \\ $$$$\left(\mathrm{3}\right)\:\left[\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right] \\ $$$$\left(\mathrm{4}\right)\:\left[−\frac{\pi}{\mathrm{2}},\:\frac{\mathrm{3}\pi}{\mathrm{2}}\right] \\ $$ Answered by mrW1…
Question Number 15263 by Tinkutara last updated on 08/Jun/17 $$\mathrm{The}\:\mathrm{equation}\:{a}\mathrm{sin}{x}\:+\:\mathrm{cos2}{x}\:=\:\mathrm{2}{a}\:−\:\mathrm{7} \\ $$$$\mathrm{possesses}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{if} \\ $$$$\left(\mathrm{1}\right)\:{a}\:>\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}\:\leqslant\:{a}\:\leqslant\:\mathrm{6} \\ $$$$\left(\mathrm{3}\right)\:{a}\:>\:\mathrm{2} \\ $$$$\left(\mathrm{4}\right)\:{a} \\ $$ Answered by ajfour…