Question Number 209768 by OmoloyeMichael last updated on 20/Jul/24 $$\boldsymbol{{Express}}\:\boldsymbol{{tan}}\left(\mathrm{3}\right)\:\boldsymbol{{in}}\:\boldsymbol{{surd}}\:\boldsymbol{{form}} \\ $$ Answered by Frix last updated on 22/Jul/24 $$\mathrm{tan}\:\left(\alpha−\beta\right)\:=\frac{\mathrm{tan}\:\alpha\:−\mathrm{tan}\:\beta}{\mathrm{1}+\mathrm{tan}\:\alpha\:\mathrm{tan}\:\beta} \\ $$$$\mathrm{Use}\:\alpha=\mathrm{18}°\:\mathrm{and}\:\beta=\mathrm{15}°.\:\mathrm{The}\:\mathrm{only}\:\mathrm{problem}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{factorize}\:\mathrm{it}… \\…
Question Number 209706 by mr W last updated on 19/Jul/24 $${find}\:{the}\:{sum}\:{of}\: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+…+\mathrm{sin}^{\mathrm{2}} \:\mathrm{60}°=? \\ $$ Answered by BaliramKumar last updated on 19/Jul/24…
Question Number 209735 by hardmath last updated on 19/Jul/24 $$\mathrm{tan}\left(\mathrm{3x}\right)\:\:+\:\:\mathrm{tan}\left(\mathrm{5x}\right)\:\:=\:\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by a.lgnaoui last updated on 20/Jul/24 $$\mathrm{voir}\:\mathrm{reponse}\:\mathrm{en}\:\mathrm{bas} \\ $$$$\:\left(\mathrm{a}\:\mathrm{l}\:\mathrm{exeption}\:\:\mathrm{d}\:'\mathrm{ereur}\:\mathrm{de}\:\mathrm{calcul}\right) \\…
Question Number 209719 by hardmath last updated on 19/Jul/24 $$\mathrm{If}: \\ $$$$\mathrm{7}^{\mathrm{243}} \:\:=\:\:\overline {\mathrm{a}…\mathrm{bc}} \\ $$$$\mathrm{Find}: \\ $$$$\mathrm{b}\centerdot\mathrm{c}\:=\:? \\ $$ Answered by MM42 last updated…
Question Number 209694 by Frix last updated on 18/Jul/24 $${x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} =\alpha^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{yz}+{z}^{\mathrm{2}} =\beta^{\mathrm{2}} \\ $$$${z}^{\mathrm{2}} +{zx}+{x}^{\mathrm{2}} =\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} \\ $$$$\mathrm{Find}\:{x}+{y}+{z}\:\mathrm{for}\:{x},\:{y},\:{z}\:\in\mathbb{R}^{+} \\ $$…
Question Number 209695 by hardmath last updated on 18/Jul/24 $$\mathrm{If}: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\right)\centerdot\sqrt{\mathrm{2}}\:=\:\mathrm{7}\centerdot\left(\mathrm{a}−\mathrm{b}−\mathrm{4}\right) \\ $$$$\mathrm{Find}: \\ $$$$\left(\mathrm{2a}\:+\:\mathrm{b}\right)\:=\:? \\ $$ Answered by mr W last updated on…
Question Number 209633 by Abdullahrussell last updated on 17/Jul/24 Answered by som(math1967) last updated on 17/Jul/24 $$\left({x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{6}{x}+\mathrm{5}\right)^{\mathrm{2}} =\mathrm{6} \\ $$$$\Rightarrow\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}\right)\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{60}{x}+\mathrm{25}\right)=\mathrm{6} \\ $$$$\Rightarrow\left({a}+\mathrm{2}\right)\left(\mathrm{12}{a}+\mathrm{25}\right)=\mathrm{6} \\…
Question Number 209580 by hardmath last updated on 15/Jul/24 $$\mathrm{If}\:\:\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} >\mathrm{0}\:\:\:\mathrm{and}\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:=\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{ln}\:\left(\frac{\mathrm{k}}{\mathrm{n}}\:+\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} \right)\:=\:? \\ $$ Answered by mr W…
Question Number 209531 by hardmath last updated on 13/Jul/24 $$\frac{\mathrm{y}^{''} }{\mathrm{y}}\:\:=\:\:\mathrm{4x}^{\mathrm{2}} \:\:+\:\:\mathrm{2} \\ $$ Commented by hardmath last updated on 13/Jul/24 $$ \\ $$Solve the…
Question Number 209542 by Spillover last updated on 13/Jul/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{15}} −{x}^{\mathrm{11}} } \\ $$$$ \\ $$$$ \\ $$ Answered by Frix last updated…