Question Number 143913 by Sravanth last updated on 19/Jun/21 $$\mathrm{If}\:\:\frac{\mathrm{cos}\:\alpha}{{cos}\:\beta}\:=\:\mathrm{m}\:\mathrm{and}\:\frac{\mathrm{cos}\:\alpha}{\mathrm{sin}\:\beta}\:=\:\mathrm{n}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta\:=\:{n}^{\mathrm{2}} \\ $$ Answered by Ar Brandon last updated on 19/Jun/21…
Question Number 12843 by tawa last updated on 04/May/17 $$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1}.\:\mathrm{and}\:\mathrm{a},\mathrm{b}\:\:\mathrm{member}\:\mathrm{of}\:\mathrm{R}.\:\mathrm{Suppose}\:\mathrm{a}\:\mathrm{is} \\ $$$$\mathrm{invertible}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:+\:\mathrm{b}\:\mathrm{is}\:\mathrm{invertible}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143909 by mathdanisur last updated on 19/Jun/21 Commented by mr W last updated on 19/Jun/21 $${i}\:{remember}\:{i}\:{solved}\:{the}\:{same} \\ $$$${question}\:{some}\:{days}\:{ago}. \\ $$ Commented by amin96…
Question Number 143904 by nadovic last updated on 19/Jun/21 Answered by Dwaipayan Shikari last updated on 19/Jun/21 $$\frac{\mathrm{1}}{\:\sqrt{\pi}}\int_{−\infty} ^{\infty} {e}^{−{x}^{\mathrm{2}} } {dx}=\mathrm{1}\:\:{e}^{\pi{i}} =−\mathrm{1} \\ $$$${p}=\mathrm{2}…
Question Number 143906 by mathdanisur last updated on 19/Jun/21 Answered by TheHoneyCat last updated on 19/Jun/21 $$\Leftrightarrow{x}^{{x}} −{y}^{{y}} ={e}.\mathrm{ln}\left(\frac{{y}}{{x}}\right)={e}\left(\mathrm{ln}\left({y}\right)−\mathrm{ln}\left({x}\right)\right) \\ $$$$\Leftrightarrow{x}^{{x}} +{e}\mathrm{ln}{x}={y}^{{y}} +{e}\mathrm{ln}{y} \\ $$$$…
Question Number 12830 by chux last updated on 03/May/17 $$\mathrm{the}\:\mathrm{LCM}\:\mathrm{and}\:\mathrm{HCF}\:\mathrm{of}\:\mathrm{30}\:\mathrm{and}\:\mathrm{a}\: \\ $$$$\mathrm{certain}\:\mathrm{number}\:\mathrm{are}\:\mathrm{150}\:\mathrm{and}\:\mathrm{5}\: \\ $$$$\mathrm{respectively}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{number} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$ Answered by RasheedSoomro…
Question Number 12829 by tawa last updated on 03/May/17 Answered by mrW1 last updated on 03/May/17 $$\left(\mathrm{1}\right) \\ $$$${let}'{s}\:{say}\:{the}\:{mean}\:{mark}\:{of}\:{the}\:\mathrm{6}\:{students} \\ $$$${who}\:{passed}\:{is}\:{x}. \\ $$$${the}\:{total}\:{mark}\:{of}\:{the}\:\mathrm{2}\:{students}\:{who} \\ $$$${failed}\:{is}\:{y}.…
Question Number 143897 by liberty last updated on 19/Jun/21 Answered by bobhans last updated on 19/Jun/21 $$\:\:\mathrm{sin}\:^{\mathrm{2}} \:\frac{\pi}{\mathrm{8}}+\mathrm{cos}\:^{\mathrm{2}} \:\frac{\pi}{\mathrm{8}}+\mathrm{cos}\:^{\mathrm{2}} \:\frac{\mathrm{5}\pi}{\mathrm{8}}+\mathrm{sin}\:^{\mathrm{2}} \:\frac{\mathrm{5}\pi}{\mathrm{8}}=\mathrm{2} \\ $$ Terms of…
Question Number 12826 by malwaan last updated on 03/May/17 $$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{1}:\:\:\mathrm{0}<\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\mathrm{x}\sqrt{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}<\:\frac{\pi^{\mathrm{2}} }{\mathrm{32}} \\ $$$$\mathrm{2}:\:\frac{\mathrm{1}}{\mathrm{2}}<\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:\mathrm{dx}\:<\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\mathrm{3}:\:\mathrm{0}<\int_{\mathrm{100}\pi} ^{\mathrm{200}\pi} \:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{x}}\:\mathrm{dx}\:<\frac{\mathrm{1}}{\mathrm{100}\pi} \\ $$…
Question Number 143899 by liberty last updated on 19/Jun/21 Answered by ajfour last updated on 19/Jun/21 $${let}\:\:{r}^{\mathrm{10}} ={z} \\ $$$${t}={z}^{\mathrm{4}} −{z}^{\mathrm{3}} +{z}^{\mathrm{2}} −{z}+\mathrm{1} \\ $$$${r}^{\mathrm{5}}…