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Question Number 13904 by tawa tawa last updated on 24/May/17 $$\mathrm{Show}\:\mathrm{that}\:\::\:\:\mathrm{sin}\left(\mathrm{50}\right)\:+\:\mathrm{sin}\left(\mathrm{40}\right)\:=\:\sqrt{\mathrm{2}}\:\mathrm{cos}\left(\mathrm{5}\right) \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 25/May/17 $$=\sqrt{\mathrm{2}}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{cos}\mathrm{40}+\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{sin}\mathrm{40}\right)=\sqrt{\mathrm{2}}{sin}\left(\mathrm{45}+\mathrm{40}\right) \\ $$$$=\sqrt{\mathrm{2}}{sin}\mathrm{85}=\sqrt{\mathrm{2}}{cos}\mathrm{5}\:\:.\blacksquare \\ $$…
Question Number 13903 by tawa tawa last updated on 24/May/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{range}\:\mathrm{0}°\:\mathrm{to}\:\mathrm{360}°\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\mathrm{sin}\left(\mathrm{3x}\right)\mathrm{sin}\left(\mathrm{x}\right)\:=\:\mathrm{2cos}\left(\mathrm{2x}\right)\:+\:\mathrm{1} \\ $$ Commented by myintkhaing last updated on 26/May/17 $${Please}\:{in}\:{the}\:{range}\:\mathrm{0}°\:{to}\:\mathrm{360}°\:{means} \\ $$$$\mathrm{0}°<{x}<\mathrm{360}°\:{or}\:\mathrm{0}°\leqslant{x}\leqslant\mathrm{360}°\:??…
Question Number 79395 by jagoll last updated on 24/Jan/20 $$\mathrm{given}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{is}\:\mathrm{a}\:\:\mathrm{point}\:\mathrm{on}\:\mathrm{circle} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{6x}+\mathrm{4y}−\mathrm{23}=\mathrm{0}. \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{4x}+\mathrm{3y}\: \\ $$ Commented by john santu last…
Question Number 144930 by alcohol last updated on 30/Jun/21 $${solve} \\ $$$$\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }={cosx} \\ $$ Answered by ArielVyny last updated on 30/Jun/21 $$−{cosx} \\…
Question Number 144914 by bobhans last updated on 30/Jun/21 $$\:\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},…