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Category: Trigonometry

tan-2-pi-7-tan-2-3pi-7-tan-2-5pi-7-

Question Number 171389 by cortano1 last updated on 14/Jun/22 $$\:\:\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{5}\pi}{\mathrm{7}}\right)=? \\ $$ Commented by Shrinava last updated on 14/Jun/22 $$\mathrm{Or}\:\mathrm{sec}^{\mathrm{2}} \:\frac{\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}} \:\frac{\mathrm{3}\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}}…

solve-for-1-period-sin-2-sin-2-sin-3-sin-3-cos-2-cos-2-cos-3-cos-3-tan-2-tan-2-tan-3-tan-3-

Question Number 40285 by MJS last updated on 18/Jul/18 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{1}\:\mathrm{period} \\ $$$$\mathrm{sin}\:\frac{\alpha}{\mathrm{2}}\:=\mathrm{sin}\:\mathrm{2}\alpha \\ $$$$\mathrm{sin}\:\frac{\beta}{\mathrm{3}}\:=\mathrm{sin}\:\mathrm{3}\beta \\ $$$$\mathrm{cos}\:\frac{\gamma}{\mathrm{2}}\:=\mathrm{cos}\:\mathrm{2}\gamma \\ $$$$\mathrm{cos}\:\frac{\delta}{\mathrm{3}}\:=\mathrm{cos}\:\mathrm{3}\delta \\ $$$$\mathrm{tan}\:\frac{\epsilon}{\mathrm{2}}\:=\mathrm{tan}\:\mathrm{2}\epsilon \\ $$$$\mathrm{tan}\:\frac{\zeta}{\mathrm{3}}\:=\mathrm{tan}\:\mathrm{3}\zeta \\ $$ Answered…

1-If-cos-4-5-and-sin-5-13-where-0-lt-lt-pi-4-Find-tan-2-2-cos-4-pi-8-cos-4-3pi-8-cos-4-5pi-8-cos-4-7pi-8-

Question Number 105764 by bobhans last updated on 31/Jul/20 $$\left(\mathrm{1}\right){If}\:\mathrm{cos}\:\left(\alpha+\beta\right)\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:{and}\:\mathrm{sin}\:\left(\alpha−\beta\right)\:=\:\frac{\mathrm{5}}{\mathrm{13}} \\ $$$${where}\:\mathrm{0}\:<\:\alpha<\:\frac{\pi}{\mathrm{4}}.\:{Find}\:\mathrm{tan}\:\mathrm{2}\alpha\:. \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right)? \\ $$ Commented by Dwaipayan Shikari last…

Question-40231

Question Number 40231 by Raj Singh last updated on 17/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jul/18 $$\frac{{cosA}−{sinA}+\mathrm{1}}{{cosA}+{sinA}−\mathrm{1}} \\ $$$${a}={sinA}\:\:\:{b}={cosA}\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1} \\ $$$$\frac{\left({b}−{a}+\mathrm{1}\right)\left({b}+{a}+\mathrm{1}\right)}{\left({b}+{a}−\mathrm{1}\right)\left({b}+{a}+\mathrm{1}\right)} \\…

If-p-sin-pi-18-sin-5pi-18-sin-7pi-18-find-the-value-of-p-

Question Number 105766 by bramlex last updated on 31/Jul/20 $${If}\:{p}\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{18}}\right)\mathrm{sin}\:\left(\frac{\mathrm{5}\pi}{\mathrm{18}}\right)\mathrm{sin}\:\left(\frac{\mathrm{7}\pi}{\mathrm{18}}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{p}. \\ $$ Answered by som(math1967) last updated on 31/Jul/20 $$\mathrm{let}\:\frac{\pi}{\mathrm{18}}=\alpha \\ $$$$\therefore\mathrm{p}=\mathrm{sin}\alpha\mathrm{sin5}\alpha\mathrm{sin7}\alpha \\…

cos-2-5x-sin-2-7x-1-

Question Number 105692 by bramlex last updated on 31/Jul/20 $$\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{5}{x}\right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{7}{x}\right)=\mathrm{1} \\ $$ Answered by john santu last updated on 31/Jul/20 $$\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{5}{x}\right)+\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{7}{x}\right)=\mathrm{1}…

cos-1-2x-cos-1-x-pi-6-find-x-

Question Number 105650 by bemath last updated on 30/Jul/20 $$\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)+\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)=\frac{\pi}{\mathrm{6}} \\ $$$${find}\:{x} \\ $$ Answered by bramlex last updated on 30/Jul/20 $$\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)=\frac{\pi}{\mathrm{6}}−\mathrm{cos}^{−\mathrm{1}}…

find-General-solution-cot-x-cot-2x-cot3x-0-

Question Number 105619 by bobhans last updated on 30/Jul/20 $${find}\:\mathcal{G}{eneral}\:{solution}\:\mathrm{cot}\:{x}+\mathrm{cot}\:\mathrm{2}{x}+\mathrm{cot3}{x}=\:\mathrm{0} \\ $$$$ \\ $$ Answered by bemath last updated on 30/Jul/20 $$\Leftrightarrow\mathrm{cot}\:\left({x}\right)+\frac{\mathrm{cot}\:^{\mathrm{2}} \left({x}\right)−\mathrm{1}}{\mathrm{2cot}\:\left({x}\right)}+\frac{\mathrm{3cot}\:\left({x}\right)−\mathrm{cot}\:^{\mathrm{3}} \left({x}\right)}{\mathrm{1}−\mathrm{3cot}\:^{\mathrm{2}} \left({x}\right)}=\:\mathrm{0}…