Question Number 41691 by avishek last updated on 11/Aug/18 $${tan}^{\mathrm{2}} \mathrm{20}+{tan}^{\mathrm{2}} \mathrm{40}+{tan}^{\mathrm{2}} \mathrm{80}=\mathrm{33} \\ $$ Answered by ajfour last updated on 12/Aug/18 $${let}\:\mathrm{tan}\:\mathrm{20}°={m} \\ $$$$\mathrm{tan}\:\mathrm{3}\theta=\frac{\mathrm{3tan}\:\theta−\mathrm{tan}\:^{\mathrm{3}}…
Question Number 172732 by depressiveshrek last updated on 30/Jun/22 $$\mathrm{sin}\theta−\mathrm{cos}\theta=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{sin}^{\mathrm{4}} \theta+\mathrm{cos}^{\mathrm{4}} \theta=? \\ $$ Answered by floor(10²Eta[1]) last updated on 30/Jun/22 $$\left(\mathrm{sin}\theta−\mathrm{cos}\theta\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{1}−\mathrm{sin}\left(\mathrm{2}\theta\right)…
Question Number 172608 by Mikenice last updated on 29/Jun/22 Answered by FelipeLz last updated on 03/Jul/22 $${f}\left({x}\right)\:=\:{x}−\mathrm{sin}\left({x}\right) \\ $$$$\int\frac{{x}\mathrm{cos}\left({x}\right)−\mathrm{sin}\left({x}\right)}{\left[{x}−\mathrm{sin}\left({x}\right)\right]^{\mathrm{2}} }{dx} \\ $$$$\int\frac{{x}\mathrm{cos}\left({x}\right)−{x}+{x}−\mathrm{sin}\left({x}\right)}{\left[{x}−\mathrm{sin}\left({x}\right)\right]^{\mathrm{2}} }{dx} \\ $$$$\int\frac{\left[{x}−\mathrm{sin}\left({x}\right)\right]−{x}\left[\mathrm{1}−\mathrm{cos}\left({x}\right)\right]}{\left[{x}−\mathrm{sin}\left({x}\right)\right]^{\mathrm{2}}…
Question Number 107018 by bemath last updated on 08/Aug/20 $$\mathcal{G}{iven}\:{f}\left({x}\right)=\frac{\mathrm{10}}{\mathrm{2}−\mathrm{sin}\:\mathrm{2}{x}}.\:{Find}\:{maximum}\:{value}\: \\ $$$${f}\left({x}\right). \\ $$ Commented by PRITHWISH SEN 2 last updated on 08/Aug/20 $$\mathrm{for}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{to}\:\mathrm{be}\:\mathrm{max}.\:\mathrm{2}−\mathrm{sin}\:\mathrm{2x}\:\mathrm{must}\:\mathrm{be}\:\mathrm{min}.\: \\…
Question Number 41444 by Rio Michael last updated on 07/Aug/18 $${Given}\:{that}\:\:\:{cos}\left(\theta\:+\:\frac{\pi}{\mathrm{3}}\right)=\:\frac{\mathrm{1}}{\mathrm{2}}\:{find}\:{the}\:{values}\:{of}\:\theta\:{inthe}\:{range}\:\:\mathrm{0}°\leqslant\:\theta\leqslant\mathrm{360}° \\ $$ Commented by maxmathsup by imad last updated on 07/Aug/18 $${cos}\left(\theta\:+\frac{\pi}{\mathrm{3}}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\:\Leftrightarrow\:{cos}\left(\theta\:+\frac{\pi}{\mathrm{3}}\right)={cos}\left(\frac{\pi}{\mathrm{3}}\right)\Leftrightarrow\theta\:+\frac{\pi}{\mathrm{3}}\:=\frac{\pi}{\mathrm{3}}\:+\mathrm{2}{k}\pi\:{or} \\ $$$$\theta\:+\frac{\pi}{\mathrm{3}}=−\frac{\pi}{\mathrm{3}}\:+\mathrm{2}{k}\pi\:\left({k}\in{Z}\right)\Leftrightarrow\:\:\theta=\mathrm{2}{k}\pi\:\:{or}\:\theta\:=−\frac{\mathrm{2}\pi}{\mathrm{3}}\:+\mathrm{2}{k}\pi\:\:{now}\:{let}\:{sove}\:{in}\left[\mathrm{0},\mathrm{2}\pi\right]…
Question Number 106958 by bemath last updated on 08/Aug/20 $$\:\:\:@{bemath}@ \\ $$$$\left(\mathrm{1}\right)\:{Given}\:\begin{cases}{{x}=\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta}\\{{y}=\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta}\end{cases} \\ $$$${maximum}\:{value}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{when}\:\alpha=… \\ $$$$\left(\mathrm{2}\right)\:{find}\:{solution}\:{set}\:{the}\:{equation} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} {x}\:+\:\mathrm{sin}\:^{\mathrm{4}} \left({x}+\frac{\pi}{\mathrm{4}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\:{where}\:{x}\:\in\:\left[\mathrm{0},\mathrm{2}\pi\right]\: \\ $$ Answered…
Question Number 106950 by bemath last updated on 08/Aug/20 $$\:\:\:\:\:\:\:\:\:\:^{@{bemath}@} \\ $$$${Given}\:\begin{cases}{\mathrm{2cos}\:{x}+\mathrm{7cos}\:{y}\:=\mathrm{5}}\\{\mathrm{2sin}\:{x}+\mathrm{7sin}\:{y}\:=\:\mathrm{6}}\end{cases} \\ $$$$\mathrm{cos}\:\left({x}−{y}\right)\:=?\: \\ $$ Answered by john santu last updated on 08/Aug/20 $$\:\:\:\:\:\:\:\:\:\blacklozenge\mathrm{JS}\lozenge…
Question Number 106944 by Rio Michael last updated on 08/Aug/20 $$\mathrm{If}\:\underset{{i}=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{sin}\:\left(\theta_{{i}} \right)\:=\:{n}\:\mathrm{then}\:\:\mathrm{cos}\:\left(\theta_{\mathrm{1}} \right)\:+\:\mathrm{cos}\:\left(\theta_{\mathrm{2}} \right)\:+\:\mathrm{cos}\:\left(\theta_{\mathrm{3}} \right)\:+\:…\:+\:\mathrm{cos}\:\left(\theta_{{n}} \right)\:=\:? \\ $$$$\mathrm{i}\:\mathrm{got}\:\mathrm{0}\:\mathrm{as}\:\mathrm{answer}.\:\mathrm{please}\:\mathrm{who}\:\mathrm{can}\:\mathrm{correct}? \\ $$ Commented by mr…
Question Number 41394 by Rio Michael last updated on 07/Aug/18 $$\left.{show}\:{that}\:{a}\right)\:\frac{\mathrm{1}−{cos}\mathrm{2}{A}}{\mathrm{1}+{cos}\mathrm{2}{A}}\:\equiv\:{tan}^{\mathrm{2}} {A} \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}\right)\:\frac{{sin}\mathrm{2}{A}}{\mathrm{1}+{cos}\mathrm{2}{A}}\equiv\:{tanA}. \\ $$ Commented by mondodotto@gmail.com last updated on 07/Aug/18 $$\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{part}}\:\boldsymbol{\mathrm{B}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{should}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{proved}} \\…
Question Number 41290 by Rio Michael last updated on 04/Aug/18 $${An}\:{electric}\:{pole}\:{PN}\:{is}\:{such}\:{that}\:{PN}=\mathrm{12}{cm}\:{where}\:{N}\:{is}\:{the}\:{top}\:{of}\:{the}\:{pole}\:{and}\:{P}\:{the}\:{base} \\ $$$$.{At}\:{a}\:{given}\:{moment}\:{of}\:{the}\:{day}\:{the}\:\boldsymbol{{shadow}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{pole}}\:{PN}'\:=\:{PN}.\:{find}\: \\ $$$$\left.{a}\right)\:{the}\:{length}\:{NN}' \\ $$$$\left.{b}\right)\:{the}\:{bearing}\:{of}\:{P}\:{from}\:{N}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…