Question Number 137530 by ZiYangLee last updated on 03/Apr/21 $$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta\right)+\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\alpha−\mathrm{sin}\:\beta\right)=\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}^{\mathrm{2}} \alpha+\mathrm{sin}^{\mathrm{2}} \beta.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\frac{\mathrm{1}}{\mathrm{2}}\right] \\ $$ Answered by mr W last updated on…
Question Number 6449 by Temp last updated on 27/Jun/16 $${x}=\mathrm{0}.\mathrm{112123123412345123456}… \\ $$$$\mathrm{decimal}\:\mathrm{pattern}:\:\mathrm{1},\:\mathrm{12},\:\mathrm{123},\:… \\ $$$$\mathrm{Can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{represented}\:\mathrm{as}\:\mathrm{a}\:\mathrm{fraction}? \\ $$$$\mathrm{or}\:\mathrm{is}\:\mathrm{this}\:\mathrm{number}\:\mathrm{trancendental}? \\ $$ Commented by prakash jain last updated on…
Question Number 137523 by SOMEDAVONG last updated on 03/Apr/21 $$\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}!−\mathrm{1}}{\mathrm{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 03/Apr/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\Gamma\left({x}+\mathrm{1}\right)−\mathrm{1}}{{x}}=\frac{\mathrm{1}−\gamma{x}−\mathrm{1}}{{x}}=−\gamma \\ $$$$\Gamma\left({x}+\mathrm{1}\right)\sim\mathrm{1}−\gamma{x}…
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Question Number 71955 by Maclaurin Stickker last updated on 22/Oct/19 Commented by Maclaurin Stickker last updated on 22/Oct/19 $${What}\:{is}\:{the}\:{value}\:{of}\:\:\frac{{AB}}{{AC}}? \\ $$ Answered by mr W…
Question Number 71944 by aliesam last updated on 22/Oct/19 Answered by mind is power last updated on 23/Oct/19 $$\mathrm{a}=\left\{\left(−\mathrm{1}\right)^{\mathrm{k}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{k}}\right);\mathrm{k}\in\mathrm{Z}\right\} \\ $$$$\mathrm{let}\:\mathrm{a}_{\mathrm{n}} \in\mathrm{a} \\ $$$$\mathrm{a}_{\mathrm{2n}}…
Question Number 137477 by Sandeep11 last updated on 03/Apr/21 Commented by MJS_new last updated on 03/Apr/21 $$\mathrm{well}\:\mathrm{just}\:\mathrm{derivate}\:\mathrm{the}\:\mathrm{answers}\:\mathrm{and}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{right}\:\mathrm{one}?! \\ $$ Answered by soumyasaha last…
Question Number 137470 by Sandeep11 last updated on 03/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137468 by ZiYangLee last updated on 03/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\left(\mathrm{cos}\:\mathrm{1}°+{i}\mathrm{sin}\:\mathrm{1}°\right)\left(\mathrm{cos}\:\mathrm{2}°+{i}\mathrm{sin}\:\mathrm{2}°\right)\ldots\left(\mathrm{cos}\:\mathrm{359}°+{i}\mathrm{sin}\:\mathrm{359}°\right). \\ $$ Answered by mr W last updated on 03/Apr/21 $$={e}^{\frac{\mathrm{1}}{\mathrm{180}}\pi{i}} {e}^{\frac{\mathrm{2}}{\mathrm{180}}\pi{i}} …{e}^{\frac{\mathrm{359}}{\mathrm{180}}\pi{i}}…
Question Number 137467 by SOMEDAVONG last updated on 03/Apr/21 Answered by Ñï= last updated on 03/Apr/21 $${I}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{{i}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}=\frac{\mathrm{1}}{{i}}\int{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} {d}\left(\mathrm{sin}^{−\mathrm{1}}…