Question Number 80941 by jagoll last updated on 08/Feb/20 $$\mathrm{cos}\:{x}−\mathrm{2cos}\:{y}=−\sqrt{\mathrm{3}} \\ $$$$\mathrm{sin}\:\left({x}−{y}\right)=\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$$${what}\:{is}\:\mathrm{sin}\:{x}−\mathrm{2sin}\:{y}\:? \\ $$ Commented by john santu last updated on 08/Feb/20 $${let}\:\mathrm{sin}\:{x}−\mathrm{2sin}\:{y}\:=\:{t}…
Question Number 15393 by Tinkutara last updated on 10/Jun/17 $$\mathrm{A}\:\mathrm{man}\:\mathrm{observes}\:\mathrm{that}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres}\:\mathrm{on}\:\mathrm{a}\:\mathrm{slope},\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{from}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{slope}\:\mathrm{is}\:\mathrm{30}°,\:\mathrm{and}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{further}\:\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres},\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{depression}\:\mathrm{of}\:\mathrm{that}\:\mathrm{point}\:\mathrm{is}\:\mathrm{45}°.\:\mathrm{The} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{inclination}\:\mathrm{of}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{with}\:\mathrm{the} \\…
Question Number 15392 by Tinkutara last updated on 10/Jun/17 $$\mathrm{Each}\:\mathrm{side}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$$\mathrm{subtends}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{60}°\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{tower}\:\mathrm{of}\:\mathrm{height}\:{h}\:\mathrm{standing}\:\mathrm{at}\:\mathrm{the}\:\mathrm{centre} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}.\:\mathrm{If}\:\mathrm{2}{a}\:\mathrm{be}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle},\:\mathrm{then}\:\frac{{a}^{\mathrm{2}} }{{h}^{\mathrm{2}} }\:=\:? \\ $$ Answered by mrW1…
Question Number 80929 by mathocean1 last updated on 08/Feb/20 $$\mathrm{show}\:\mathrm{that} \\ $$$${cos}\frac{\pi}{\mathrm{7}}\mathrm{cos}\frac{\mathrm{2}\pi}{\mathrm{7}}\mathrm{cos}\frac{\mathrm{4}\pi}{\mathrm{7}}=−\frac{\mathrm{1}}{\mathrm{8}} \\ $$ Commented by jagoll last updated on 08/Feb/20 $${let}\:{x}\:=\frac{\pi}{\mathrm{7}} \\ $$$$\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{4}{x}\:×\frac{\mathrm{2sin}\:{x}}{\mathrm{2sin}\:{x}}\:= \\…
Question Number 15384 by Tinkutara last updated on 10/Jun/17 $$\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…