Question Number 171574 by cortano1 last updated on 18/Jun/22 Answered by mr W last updated on 18/Jun/22 Commented by mr W last updated on 18/Jun/22…
Question Number 171479 by som(math1967) last updated on 16/Jun/22 $$\:\boldsymbol{{tan}}^{\mathrm{2}} \frac{\boldsymbol{\pi}}{\mathrm{7}}\:+\boldsymbol{{tan}}^{\mathrm{2}} \frac{\mathrm{3}\boldsymbol{\pi}}{\mathrm{7}}\:+\boldsymbol{{tan}}^{\mathrm{2}} \frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{7}}=? \\ $$ Commented by som(math1967) last updated on 16/Jun/22 $$\boldsymbol{{re}}\:\boldsymbol{{post}}\:\boldsymbol{{of}}\:\:\boldsymbol{{qno}}.\mathrm{171389} \\ $$…
Question Number 105916 by bobhans last updated on 02/Aug/20 $${prove}\:{that}\:\mathrm{cot}\:{x}.\:\mathrm{cot}\:\mathrm{2}{x}\:+\mathrm{cot}\:\mathrm{2}{x}.\:\mathrm{cot}\:\mathrm{3}{x}+\mathrm{2}\:= \\ $$$$\mathrm{cot}\:{x}.\left(\mathrm{cot}\:{x}−\mathrm{cot}\:\mathrm{3}{x}\right)\: \\ $$ Answered by bemath last updated on 01/Aug/20 $$\mathrm{cot}\:{x}\:\mathrm{cot}\:\mathrm{2}{x}\:+\:\mathrm{cot}\:\mathrm{2}{x}\:\mathrm{cot}\:\mathrm{3}{x}\:=\: \\ $$$$\mathrm{cot}\:\mathrm{2}{x}\:\left(\mathrm{cot}\:{x}+\mathrm{cot}\:\mathrm{3}{x}\right)= \\…
Question Number 105861 by bemath last updated on 01/Aug/20 $$\mathcal{G}{iven}\:\begin{cases}{\mathrm{sin}\:\mathrm{2}{x}−\mathrm{sin}\:\mathrm{2}{y}=−\frac{\mathrm{5}}{\mathrm{12}}}\\{\mathrm{cos}\:\left({x}+{y}\right)=\:−\frac{\mathrm{2}}{\mathrm{3}}\mathrm{sin}\:\left({x}−{y}\right)}\end{cases} \\ $$$${where}\:\mathrm{0}\:<\:{x}−{y}<\pi. \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{cos}\:\left({x}+{y}\right)+\mathrm{2sin}\:\left({x}−{y}\right) \\ $$ Commented by PRITHWISH SEN 2 last updated on 01/Aug/20…
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 $$\mathrm{Or}\:\mathrm{sec}^{\mathrm{2}} \:\frac{\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}} \:\frac{\mathrm{3}\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}}…
Question Number 40285 by MJS last updated on 18/Jul/18 $$\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…
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 Number 40231 by Raj Singh last updated on 17/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jul/18 $$\frac{{cosA}−{sinA}+\mathrm{1}}{{cosA}+{sinA}−\mathrm{1}} \\ $$$${a}={sinA}\:\:\:{b}={cosA}\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1} \\ $$$$\frac{\left({b}−{a}+\mathrm{1}\right)\left({b}+{a}+\mathrm{1}\right)}{\left({b}+{a}−\mathrm{1}\right)\left({b}+{a}+\mathrm{1}\right)} \\…
Question Number 105766 by bramlex last updated on 31/Jul/20 $${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 $$\mathrm{let}\:\frac{\pi}{\mathrm{18}}=\alpha \\ $$$$\therefore\mathrm{p}=\mathrm{sin}\alpha\mathrm{sin5}\alpha\mathrm{sin7}\alpha \\…
Question Number 105759 by bramlex last updated on 31/Jul/20 $${If}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{solution}\:{of} \\ $$$${equation}\:{a}\:\mathrm{tan}\:\theta\:+\:{b}\:\mathrm{sec}\:\theta\:=\:{c}\:.\: \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{tan}\:\left(\alpha+\beta\right). \\ $$ Commented by bramlex last updated on 31/Jul/20 $${thx}\:{both} \\…