Question Number 27958 by bmind4860 last updated on 17/Jan/18 $${For}\:\alpha\in{R},\:{cos}\alpha{cosx}+{siny}\geqslant{sinx},\:\forall{x}\in{R}, \\ $$$${then}\:{find}\:{the}\:{sum}\:{of}\:{the}\:{possible}\:{values} \\ $$$${of}\:{sin}\alpha+{siny}. \\ $$ Answered by ajfour last updated on 17/Jan/18 $$\:\:\:\:\mathrm{sin}\:{y}\:\geqslant\:\mathrm{sin}\:{x}−\mathrm{cos}\:\alpha\mathrm{cos}\:{x} \\…
Question Number 159030 by cortano last updated on 12/Nov/21 $$\:\left(\mathrm{arcsin}\:\left(\mathrm{cos}\:\mathrm{93}°\right)\right)^{\mathrm{2}} =? \\ $$ Answered by mr W last updated on 12/Nov/21 $$\mathrm{cos}\:\mathrm{93}°=−\mathrm{sin}\:\mathrm{3}°=−\mathrm{sin}\:\left(\frac{\pi}{\mathrm{60}}\right) \\ $$$${arcsin}\left(\mathrm{cos}\:\mathrm{93}°\right)={arcsin}\left(−\mathrm{sin}\:\frac{\pi}{\mathrm{60}}\right)=−\frac{\pi}{\mathrm{60}} \\…
Question Number 159012 by alcohol last updated on 11/Nov/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 27851 by v7277668420 last updated on 15/Jan/18 Commented by bmind4860 last updated on 15/Jan/18 $${use}\:{identity}\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} =\left({a}+{b}\right)\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{ab}\right) \\ $$ Commented by…
Question Number 27850 by v7277668420 last updated on 15/Jan/18 Answered by bmind4860 last updated on 15/Jan/18 $${a}^{\mathrm{2}} {sec}^{\mathrm{2}} \theta−{b}^{\mathrm{2}} \left({sec}^{\mathrm{2}} \theta−\mathrm{1}\right)={c}^{\mathrm{2}} \\ $$$${after}\:{rearranging}\:{we}\:{have} \\ $$$${sec}^{\mathrm{2}}…
Question Number 27844 by bmind4860 last updated on 15/Jan/18 $${For}\:\alpha\epsilon{R},\:{cos}\alpha{cosx}+{siny}\geqslant{sinx},\:{then} \\ $$$${find}\:{the}\:{sum}\:{of}\:{the}\:{possible}\:{values}\:{of} \\ $$$${sin}\alpha+{siny}. \\ $$ Commented by bmind4860 last updated on 16/Jan/18 $${please}\:{help} \\…
Question Number 27843 by bmind4860 last updated on 15/Jan/18 $${sinx}+{sin}\mathrm{3}{x}+{sin}\sqrt{{x}}=\mathrm{0},\:{then}\:{find}\:{the}\: \\ $$$${general}\:{solution}? \\ $$ Commented by abdo imad last updated on 17/Jan/18 $${let}\:{put}\:\sqrt{{x}}={t}\:\:\:{e}\Leftrightarrow\:\:{sint}\:+\:{sin}\left({t}^{\mathrm{2}} \right)\:\:+{sin}\left(\mathrm{3}{t}^{\mathrm{2}} \right)\:{general}\:{case}…
Question Number 27840 by bmind4860 last updated on 15/Jan/18 $${If}\:{xcos}\theta={ycos}\left(\theta+\frac{\mathrm{2}\pi}{\mathrm{3}}\right)={zcos}\left(\theta+\frac{\mathrm{4}\pi}{\mathrm{3}}\right),{then} \\ $$$${the}\:{value}\:{of}\:{xy}+{yz}+{zx}. \\ $$ Answered by ajfour last updated on 15/Jan/18 $${let}\:\:\:\:{x}\mathrm{cos}\:\theta={y}\mathrm{cos}\:\left(\theta+\frac{\mathrm{2}\pi}{\mathrm{3}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={z}\mathrm{cos}\:\left(\theta+\frac{\mathrm{4}\pi}{\mathrm{3}}\right)={r}\: \\…
Question Number 27821 by bmind4860 last updated on 15/Jan/18 $${If}\:\alpha\:{and}\:\beta\:{satisfy}\:{sin}\alpha{cos}\beta=\:−\frac{\mathrm{1}}{\mathrm{2}}\:{then} \\ $$$${the}\:{greatest}\:{value}\:{of}\:\mathrm{2}{cos}\alpha{sin}\beta \\ $$ Answered by ajfour last updated on 15/Jan/18 $$\mathrm{sin}\:\alpha\mathrm{cos}\:\beta=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{2sin}\:\alpha\mathrm{cos}\:\beta=−\mathrm{1} \\…
Question Number 27820 by bmind4860 last updated on 15/Jan/18 $${If}\:{A},{B}\epsilon\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\right)\:{such}\:{that}\:\mathrm{3}{sin}^{\mathrm{2}} {A}+\mathrm{2}{sin}^{\mathrm{2}} {B}=\mathrm{1} \\ $$$${and}\:\mathrm{3}{sin}\mathrm{2}{A}−\mathrm{2}{sin}\mathrm{2}{B}=\mathrm{0},\:{find}\:{the}\:{value}\:{of}\:{A}+{B}. \\ $$ Answered by ajfour last updated on 15/Jan/18 $$\frac{\mathrm{3}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{A}\right)+\mathrm{1}−\mathrm{cos}\:\mathrm{2}{B}=\mathrm{1} \\…