Question Number 144914 by bobhans last updated on 30/Jun/21 $$\:\mathrm{If}\:\frac{\mathrm{1}+\mathrm{tan}\:\mathrm{4}\sqrt{\theta}}{\mathrm{1}−\mathrm{tan}\:\mathrm{4}\sqrt{\theta}}\:=\:\mathrm{tan}\:\theta\:,\:\mathrm{then}\:\mathrm{find}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\left(\theta+\mathrm{11}\sqrt{\theta}\:\right). \\ $$ Answered by imjagoll last updated on 30/Jun/21 Answered by mr W…
Question Number 13842 by Tinkutara last updated on 24/May/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{sin}\:\mathrm{5}{x}\:\mathrm{cos}\:\mathrm{3}{x}\:=\:\mathrm{sin}\:\mathrm{6}{x}\:\mathrm{cos}\:\mathrm{2}{x}, \\ $$$${x}\:\in\:\left[\mathrm{0},\:\pi\right] \\ $$ Answered by myintkhaing last updated on 24/May/17 $${five}\:{solutions} \\…
Question Number 13840 by Tinkutara last updated on 24/May/17 $$\mathrm{Solve}: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{tan}{x}\:+\:\mathrm{sec}{x}\:=\:\mathrm{2cos}{x} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{sin}\theta\:+\:\mathrm{tan}\theta\:−\:\mathrm{sin2}\theta\:=\:\mathrm{0} \\ $$ Answered by ajfour last updated on 24/May/17 $$\left({a}\right) \\…
Question Number 13835 by Tinkutara last updated on 24/May/17 Commented by Tinkutara last updated on 24/May/17 $$\mathrm{Answer}\:\mathrm{given}\:\mathrm{is}\:\mathrm{2}{n}\pi\:−\:\frac{\mathrm{3}\pi}{\mathrm{4}}\:<\:\frac{{A}}{\mathrm{2}}\:<\:\mathrm{2}{n}\pi\:−\:\frac{\pi}{\mathrm{4}} \\ $$ Answered by ajfour last updated on…
Question Number 79320 by jagoll last updated on 24/Jan/20 $$\mathrm{what}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{sec}\:\left(\mathrm{x}\right)+\mathrm{cosec}\:\left(\mathrm{x}\right)? \\ $$ Commented by mr W last updated on 24/Jan/20 $${y}=\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}} \\ $$$${it}\:{has}\:{no}\:{maximum}\:{and}\:{no}\:{minimum},…
Question Number 144828 by mathlove last updated on 29/Jun/21 $$\mathrm{2sin}\:\mathrm{17}{x}+\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{5}{x}+\mathrm{sin}\:\mathrm{5}{x}=\mathrm{0} \\ $$$${x}=? \\ $$ Answered by liberty last updated on 30/Jun/21 $$\mathrm{2sin}\:\mathrm{17x}\:+\:\mathrm{2cos}\:\left(\mathrm{5x}−\frac{\pi}{\mathrm{6}}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{cos}\:\left(\mathrm{5x}−\frac{\pi}{\mathrm{6}}\right)=−\mathrm{sin}\:\mathrm{17x} \\…
Question Number 144829 by mathlove last updated on 29/Jun/21 $$\mathrm{sin}\:^{\mathrm{3}} {x}+\mathrm{cos}\:^{\mathrm{3}} {x}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{2}} {x} \\ $$$${x}=? \\ $$ Answered by ajfour last updated on 29/Jun/21 $$\left(\mathrm{1}−{s}^{\mathrm{2}}…
Question Number 144833 by gsk2684 last updated on 29/Jun/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\alpha\:\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{4}}{\mathrm{sin}\:\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}=\alpha\: \\ $$$$\mathrm{has}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{solution}\:\mathrm{in}\:\left(\mathrm{0}\:\frac{\Pi}{\mathrm{2}}\right) \\ $$ Answered by liberty last updated on 29/Jun/21 $$\alpha=\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{4}}{\mathrm{sin}\:\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{let}\:\mathrm{u}=\mathrm{sin}\:\mathrm{x}\:\Rightarrow\mathrm{f}\left(\mathrm{u}\right)=\mathrm{4u}^{−\mathrm{1}} +\left(\mathrm{1}−\mathrm{u}\right)^{−\mathrm{1}}…
Question Number 144821 by mathlove last updated on 29/Jun/21 $$\mathrm{tan}\:\mathrm{193}={k} \\ $$$$\mathrm{cos}\:\mathrm{167}=? \\ $$ Commented by ajfour last updated on 29/Jun/21 $${are}\:{the}\:{angles}\:{in}\:{degree}\:{measure}? \\ $$ Terms…
Question Number 144822 by mathlove last updated on 29/Jun/21 $$\mathrm{sin}\:^{\mathrm{3}} {x}\mathrm{cos}\:{x}−\mathrm{cos}\:^{\mathrm{3}} {x}\mathrm{sin}\:{x}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${x}=? \\ $$ Answered by ajfour last updated on 29/Jun/21 $$\mathrm{2sin}\:{x}\mathrm{cos}\:{x}\left(\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{cos}\:^{\mathrm{2}}…