Question Number 11042 by Mahmoud A.R last updated on 09/Mar/17 $$\int{cos}\left({x}\right)\sqrt{\frac{{sin}\left({x}\right)+\mathrm{1}}{{sin}\left({x}\right)−\mathrm{1}}\:}\:{dx} \\ $$ Answered by ajfour last updated on 09/Mar/17 $$\:\:\int\mathrm{cos}\:\left({x}\right)\sqrt{−\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{sin}\:{x}}}\:{dx} \\ $$$$=\sqrt{−\mathrm{1}}\:\int\mathrm{cos}\:\left({x}\right)\sqrt{\frac{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)}{\left(\mathrm{1}−\mathrm{sin}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)}}\:{dx} \\ $$$$=\:{i}\int\mathrm{cos}\:\left({x}\right)\left(\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\right){dx}…
Question Number 142115 by mathmax by abdo last updated on 26/May/21 $$\mathrm{simplify}\:\:\mathrm{A}_{\mathrm{n}} \left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}\right)^{\mathrm{n}} +\left(\mathrm{1}−\mathrm{ix}\right)^{\mathrm{n}} \:\:\:\mathrm{x}\:\mathrm{from}\:\mathrm{C} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 76576 by Rio Michael last updated on 28/Dec/19 $${Compute}\:{the}\:{Gcd}\:\left({greatest}\:{common}\:{divisor}\right) \\ $$$${of}\:\:\mathrm{45}\:{and}\:\mathrm{1287}\: \\ $$ Answered by john santu last updated on 28/Dec/19 $$\mathrm{45}\:=\:\mathrm{3}^{\mathrm{2}} ×\mathrm{5}…
Question Number 76577 by Rio Michael last updated on 28/Dec/19 $$\:{given}\:{a}\:{sequence}\:{defined}\:{by}\:\:\left\{\frac{\mathrm{3}{n}}{\mathrm{2}{n}+\:\mathrm{5}}\right\}_{{n}=\mathrm{1}} ^{\infty} ,\:{does}\:{this}\: \\ $$$${sequence}\:{converge}\:{or}\:{diverge},\:{explain} \\ $$ Answered by john santu last updated on 28/Dec/19…
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Question Number 76575 by Rio Michael last updated on 28/Dec/19 $${define}\:{the}\:{concept}\:{of}\:{a}\:\boldsymbol{{contingency}} \\ $$$${Which}\:{of}\:{the}\:{following}\:{is}\:{a}\:{contingency}\: \\ $$$${and}\:{which}\:{is}\:{a}\:{tautology} \\ $$$$\left.\mathrm{1}\right)\:\left({P}\:\Rightarrow\sim{P}\right)\:\vee\:{Q}\:\: \\ $$$$\left.\mathrm{2}\right)\:\left({P}\:\Rightarrow\:\sim{P}\right)\:\Rightarrow\:{Q} \\ $$ Answered by benjo 1/2…
Question Number 76572 by john santu last updated on 28/Dec/19 $${how}\:{do}\:{you}\:{find}\:{the}\:{least}\:{value}\:{of}\:{x}^{\mathrm{2}} \\ $$$$+\mathrm{2}{xy}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}{y}\:{using}\:{the}\: \\ $$$${concepts}\:{of}\:{algebra}\:{or}\:{calculus}?\: \\ $$ Answered by benjo 1/2 santuyy last updated…
Question Number 11036 by suci last updated on 08/Mar/17 $${l}\underset{{n}\rightarrow\sim} {{i}m}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{8}{n}^{\mathrm{2}} }{{n}^{\mathrm{4}} +\mathrm{1}}\:=….? \\ $$ Commented by FilupS last updated on 08/Mar/17 $${S}=\underset{{n}\rightarrow\infty}…
Question Number 142105 by PRITHWISH SEN 2 last updated on 26/May/21 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms} \\ $$$$\mathrm{sin}\:\theta−\mathrm{sin}\:\mathrm{2}\theta+\mathrm{sin}\:\mathrm{3}\theta−…….. \\ $$ Answered by Dwaipayan Shikari last updated on 26/May/21 $$\underset{{n}=\mathrm{1}}…