Question Number 18036 by tawa tawa last updated on 14/Jul/17 $$\mathrm{solve}: \\ $$$$ \\ $$$$\mathrm{4cos}\left(\mathrm{x}\right)\:+\:\mathrm{2sin}\left(\mathrm{x}\right)\:=\:\mathrm{2}\:+\:\sqrt{\mathrm{3}} \\ $$ Commented by ajfour last updated on 14/Jul/17 $$\mathrm{several}\:\mathrm{solutions}.…
Question Number 18003 by Tinkutara last updated on 13/Jul/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}{A}\centerdot\mathrm{cos2}{A}\centerdot\mathrm{cos2}^{\mathrm{2}} {A}\:…..\:\mathrm{cos}\left(\mathrm{2}^{{n}\:−\:\mathrm{1}} {A}\right), \\ $$$$\mathrm{where}\:{A}\:\in\:{R}\:\mathrm{may}\:\mathrm{be} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:−\mathrm{1} \\ $$$$\left(\mathrm{4}\right)\:\frac{\mathrm{sin}\:\mathrm{2}^{{n}} \:{A}}{\mathrm{2}^{{n}} \:\mathrm{sin}\:{A}} \\…
Question Number 17983 by alex041103 last updated on 13/Jul/17 $${Evaluate}\:{cos}\left(\mathrm{20}°\right){cos}\left(\mathrm{40}°\right){cos}\left(\mathrm{80}°\right). \\ $$$${This}\:{question}\:{is}\:{just}\:{for}\:{fun}\:{and}\:{practice}. \\ $$$${Evryone}\:{who}\:{wants}\:{can}\:{answer}\:{this}\:{question}. \\ $$ Answered by ajfour last updated on 13/Jul/17 $$\mathrm{cos}\:\mathrm{20}°\mathrm{cos}\:\mathrm{40}°\mathrm{cos}\:\mathrm{80}°= \\…
Question Number 83513 by jagoll last updated on 03/Mar/20 $$\mathrm{If}\:\mathrm{m}\:\mathrm{tan}\:\left(\theta−\mathrm{30}^{\mathrm{o}} \right)\:=\:\mathrm{n}\:\mathrm{tan}\:\left(\theta+\mathrm{12}^{\mathrm{o}} \right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{cos}\:\mathrm{2}\theta\:=\:\frac{\mathrm{m}+\mathrm{n}}{\mathrm{2}\left(\mathrm{m}−\mathrm{n}\right)} \\ $$ Commented by mind is power last updated on 04/Mar/20…
Question Number 17921 by Tinkutara last updated on 12/Jul/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\left(\mathrm{3}\:−\:\mathrm{tan}^{\mathrm{2}} \mathrm{1}°\right)\left(\mathrm{3}\:−\:\mathrm{tan}^{\mathrm{2}} \mathrm{2}°\right)\left(\mathrm{3}\:−\:\mathrm{tan}^{\mathrm{2}} \mathrm{3}°\right)….\left(\mathrm{3}\:−\:\mathrm{tan}^{\mathrm{2}} \mathrm{89}°\right) \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by Tinkutara last updated…
Question Number 83430 by jagoll last updated on 02/Mar/20 $$\mathrm{prove}\:\mathrm{that}? \\ $$$$\mathrm{sin}\:\mathrm{3}\theta\:\mathrm{sin}^{\mathrm{3}} \:\theta\:+\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:^{\mathrm{3}} \theta\:=\:\: \\ $$$$\mathrm{cos}\:^{\mathrm{3}} \:\left(\mathrm{2}\theta\right) \\ $$ Answered by mind is power last…
Question Number 83425 by jagoll last updated on 02/Mar/20 $$\frac{\mathrm{tan}\:\mathrm{3a}}{\mathrm{tan}\:\mathrm{a}}\:=\:\mathrm{k} \\ $$$$\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{sin}\:\mathrm{3a}}{\mathrm{sin}\:\mathrm{a}}\:=\:\frac{\mathrm{2k}}{\mathrm{k}−\mathrm{1}} \\ $$ Commented by jagoll last updated on 02/Mar/20 $$\mathrm{tan}\:\mathrm{3a}\:=\:\mathrm{k}\:\mathrm{tan}\:\mathrm{a} \\ $$$$\frac{\mathrm{3tan}\:\mathrm{a}−\mathrm{tan}\:^{\mathrm{3}} \mathrm{a}}{\mathrm{1}−\mathrm{3tan}\:^{\mathrm{2}}…
Question Number 17866 by Tinkutara last updated on 11/Jul/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{5}{A}\:=\:\mathrm{5}\:\mathrm{cos}^{\mathrm{4}} \:{A}\:\mathrm{sin}\:{A}\:− \\ $$$$\mathrm{10}\:\mathrm{cos}^{\mathrm{2}} \:{A}\:\mathrm{sin}^{\mathrm{3}} \:{A}\:+\:\mathrm{sin}^{\mathrm{5}} \:{A} \\ $$ Answered by alex041103 last updated on 13/Jul/17…
Question Number 83352 by jagoll last updated on 01/Mar/20 $$\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)\left(\mathrm{1}−\mathrm{cos}\:\left(\mathrm{x}\right)\right)}\:=\:−\mathrm{sin}\:\left(−\mathrm{x}\right)−\mathrm{5cos}\:\left(\mathrm{x}\right) \\ $$ Commented by jagoll last updated on 01/Mar/20 $$\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}\:=\:\mathrm{sin}\:\left(\mathrm{x}\right)−\mathrm{5cos}\:\left(\mathrm{x}\right) \\ $$$$\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} \:}=\:\mathrm{sin}\:\left(\mathrm{x}\right)−\mathrm{5cos}\:\left(\mathrm{x}\right) \\…
Question Number 17815 by Tinkutara last updated on 11/Jul/17 $$\mathrm{For}\:{x}\:\in\:\left(\mathrm{0},\:\pi\right),\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:{x}\:+\:\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}\:−\:\mathrm{sin}\:\mathrm{3}{x}\:=\:\mathrm{3}\:\mathrm{has} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Infinitely}\:\mathrm{many}\:\mathrm{solutions} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Three}\:\mathrm{solutions} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{One}\:\mathrm{solution} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{No}\:\mathrm{solution} \\ $$ Commented by alex041103…