Question Number 94882 by i jagooll last updated on 21/May/20 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{tan}\:\theta+\mathrm{tan}\:\mathrm{2}\theta+\mathrm{tan}\:\mathrm{3}\theta\:=\: \\ $$$$\mathrm{tan}\:\theta.\mathrm{tan}\:\mathrm{2}\theta.\mathrm{tan}\:\mathrm{3}\theta\: \\ $$ Answered by john santu last updated on 21/May/20…
Question Number 160411 by nadovic last updated on 29/Nov/21 $$\:\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{tan}\:\mathrm{58}°\mathrm{tan}\:\mathrm{32}°\:=\:\mathrm{1} \\ $$ Answered by TheSupreme last updated on 29/Nov/21 $${tan}\left(\alpha\right){tan}\left(\frac{\pi}{\mathrm{2}}−\alpha\right)={tan}\left(\alpha\right){cotan}\left(\alpha\right)=\mathrm{1} \\ $$$$ \\ $$ Terms…
Question Number 94803 by i jagooll last updated on 21/May/20 Answered by john santu last updated on 21/May/20 Commented by i jagooll last updated on…
Question Number 29249 by ajfour last updated on 05/Feb/18 Commented by ajfour last updated on 05/Feb/18 $${Find}\:{side}\:{lengths}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}\:\:{of}\:\bigtriangleup{ABC} \\ $$$${in}\:{terms}\:{of}\:\boldsymbol{{r}}_{\mathrm{1}} ,\:\boldsymbol{{r}}_{\mathrm{2}} ,\:{and}\:\boldsymbol{{r}}_{\mathrm{3}} . \\ $$$${We}\:{may}\:{call}\:{r}_{\mathrm{1}} \:{as}\:\boldsymbol{{p}},\:…
Question Number 29173 by abdo imad last updated on 04/Feb/18 $${find}\:{cos}\left(\mathrm{5}\alpha\right)\:{interms}\:{of}\:{cos}\alpha\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$${cos}\left(\frac{\pi}{\mathrm{10}}\right). \\ $$ Answered by ajfour last updated on 05/Feb/18 $$\mathrm{cos}\:\mathrm{5}\alpha\:=\mathrm{cos}\:\mathrm{3}\alpha\:\mathrm{cos}\:\mathrm{2}\alpha−\mathrm{sin}\:\mathrm{3}\alpha\:\mathrm{sin}\:\mathrm{2}\alpha \\ $$$$=\left(\mathrm{4cos}\:^{\mathrm{3}}…
Question Number 29131 by $@ty@m last updated on 04/Feb/18 $${If}\:\mathrm{tan}^{\mathrm{2}} {a}\mathrm{tan}\:^{\mathrm{2}} {b}+\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}+\mathrm{tan}^{\mathrm{2}} {c}\mathrm{tan}\:^{\mathrm{2}} {a} \\ $$$$+\mathrm{2tan}^{\mathrm{2}} {a}\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}=\mathrm{1} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}: \\ $$$$\mathrm{sin}\:^{\mathrm{2}}…
Question Number 29111 by gyugfeet last updated on 04/Feb/18 $$\mathrm{cos}^{\mathrm{3}} {x}.\mathrm{sin}\:^{\mathrm{2}} {x}=\mathrm{1}/\mathrm{16}\left(\mathrm{2cos}\:{x}−\mathrm{cos}\:\mathrm{3}{x}−\mathrm{cos}\:\mathrm{5}{x}\right) \\ $$ Commented by abdo imad last updated on 04/Feb/18 $${another}\:{method} \\ $$$${cos}^{\mathrm{3}}…
Question Number 160165 by cortano last updated on 25/Nov/21 $$\:\:\mathrm{7}+\mathrm{4sin}\:{x}\mathrm{cos}\:{x}+\frac{\mathrm{3}}{\mathrm{2}}\left(\mathrm{cot}\:{x}+\mathrm{tan}\:{x}\right)=\mathrm{0}\: \\ $$ Commented by cortano last updated on 25/Nov/21 Answered by som(math1967) last updated on…
Question Number 94523 by peter frank last updated on 19/May/20 Commented by PRITHWISH SEN 2 last updated on 19/May/20 $$\mathrm{By}\:\mathrm{Napier}'\mathrm{s}\:\mathrm{Analogy}\: \\ $$$$\mathrm{for}\:\mathrm{any}\bigtriangleup\mathrm{ABC} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\mathrm{B}}−\boldsymbol{\mathrm{C}}}{\mathrm{2}}\:=\frac{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{c}}}{\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}}\:\boldsymbol{\mathrm{cot}}\frac{\boldsymbol{\mathrm{A}}}{\mathrm{2}} \\…
Question Number 160050 by tounghoungko last updated on 24/Nov/21 Answered by mindispower last updated on 24/Nov/21 $${cos}\left({a}\right)+{cos}\left({b}\right)=\mathrm{2}{cos}\left(\frac{{a}−{b}}{\mathrm{2}}\right){cos}\left(\frac{{a}+{b}}{\mathrm{2}}\right) \\ $$$${sin}\left({a}\right)+\mathrm{sin}\left(\mathrm{b}\right)=\mathrm{2cos}\left(\frac{\mathrm{a}−\mathrm{b}}{\mathrm{2}}\right)\mathrm{sin}\left(\frac{\mathrm{a}+\mathrm{b}}{\mathrm{2}}\right) \\ $$$$\Leftrightarrow\frac{{cos}\left(\mathrm{3}{x}\right)\left(\mathrm{2}{cos}\left(\mathrm{5}{x}\right)+\mathrm{1}\right)}{{cos}\left(\mathrm{3}{x}\right)\left(\mathrm{2}{sin}\left(\mathrm{5}{x}\right)+\mathrm{1}\right)}=\mathrm{1} \\ $$$$\forall{x}\in\mathbb{R}−\left\{{cos}\left(\mathrm{3}{x}\right)=\mathrm{0}\right\} \\ $$$$\Leftrightarrow{sin}\left(\mathrm{5}{x}\right)={cos}\left(\mathrm{5}{x}\right)\:{easy}\:{now}…