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Author: Tinku Tara

If-sin-1-sin-sin-sin-1-sin-sin-pi-2-find-the-value-of-sin-2-sin-2-1-2-

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-71993

Question Number 71993 by TawaTawa last updated on 23/Oct/19 Answered by mind is power last updated on 23/Oct/19 $$\mathrm{let}\angle\:\mathrm{A}\overset{} {\mathrm{C}E}=\angle\mathrm{ADE}=\mathrm{x} \\ $$$$\Rightarrow\angle\mathrm{ECD}=\mathrm{3x}−\mathrm{x}=\mathrm{2x}\Rightarrow\mathrm{EC}=\mathrm{ED}\:\:\mathrm{ECD}\:\mathrm{isocel}\:\mathrm{Triangl} \\ $$$$\angle\mathrm{ADC}=\angle\mathrm{EDC}−\angle\mathrm{EDA}=\mathrm{2x}−\mathrm{x}=\mathrm{x} \\…

Question-71986

Question Number 71986 by rajesh4661kumar@gmail.com last updated on 23/Oct/19 Answered by mind is power last updated on 23/Oct/19 $$\mathrm{not}\:\mathrm{unique}\:\mathrm{angle} \\ $$$$\mathrm{XY}=\left\{\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\in\mathbb{R}^{\mathrm{3}} :\mathrm{z}=\mathrm{0}\right\} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{vecror}\:\mathrm{and}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{not}\:\mathrm{defind}\: \\…

L-lim-x-0-x-1-x-

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}…

x-0-112123123412345123456-decimal-pattern-1-12-123-Can-this-be-represented-as-a-fraction-or-is-this-number-trancendental-

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…