Question Number 139409 by henderson last updated on 26/Apr/21 $$\mathrm{hi}\:! \\ $$$$\mathrm{prove}\:\mathrm{this}\::\: \\ $$$${cos}\:\frac{\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{4}\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{6}\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{9}\pi}{\mathrm{10}}\:=\:\mathrm{0}. \\ $$$$\left(\mathrm{by}\:\mathrm{the}\:\mathrm{easiest}\:\mathrm{possible}\:\mathrm{way}…!\right) \\ $$ Answered by mr W last updated on…
Question Number 8338 by tawakalitu last updated on 09/Oct/16 Commented by tawakalitu last updated on 09/Oct/16 $$\mathrm{find}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{and}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{resultant}\:\mathrm{of}\:\mathrm{the}\:\mathrm{forces}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{diagram} \\ $$ Answered by ridwan balatif…
Question Number 73872 by azizullah last updated on 16/Nov/19 Answered by $@ty@m123 last updated on 16/Nov/19 $${Rebate}\:{means}\:{part}\:{of}\:{income}\:{on} \\ $$$${which}\:{Income}\:{Tax}\:{is}\:{exempted}. \\ $$$${ATQ}, \\ $$$${Annual}\:{Income}={Rs}.\:\mathrm{8000}×\mathrm{12} \\ $$$$\:\:=\mathrm{96000}…
Question Number 8336 by Rasheed Soomro last updated on 08/Oct/16 $$\mathrm{Determine}\:\mathrm{smallest}\:\mathrm{n}\left(\neq\mathrm{0}\right),\:\mathrm{for}\:\mathrm{which} \\ $$$$\left(\omega+\mathrm{i}\right)^{\mathrm{n}} =\mathrm{1}. \\ $$ Commented by prakash jain last updated on 08/Oct/16 $${w}=\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{3}}+{i}\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{3}}=−\frac{\mathrm{1}}{\mathrm{2}}+{i}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}…
Question Number 139404 by mnjuly1970 last updated on 26/Apr/21 $$\:\:\:\:\: \\ $$$$\:\:\:#\:{Question}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{proof}\:::\:\underset{{n}=−\infty} {\overset{\:\infty} {\sum}}\left(\:\frac{{sin}\left({n}\right)}{{n}}\:\right)^{\mathrm{2}} =\pi \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…….\:{nice}\:.{calculus}\:……\:\:\:\:\: \\ $$ Answered by Dwaipayan Shikari…
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Question Number 139402 by mathmax by abdo last updated on 26/Apr/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{log}^{\mathrm{2}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 139399 by mathsuji last updated on 26/Apr/21 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{{log}\left({sin}\left({x}/\mathrm{2}\right)\right)+{log}\left({cos}\left({x}/\mathrm{2}\right)\right)}{\:\sqrt{\mathrm{2}}\centerdot{cos}\left(\pi/\mathrm{4}−{x}/\mathrm{2}\right)}\:{dx} \\ $$ Answered by Ar Brandon last updated on 26/Apr/21 $$\mathrm{Let}\:{u}=\frac{\pi}{\mathrm{2}}−{x} \\ $$…
Question Number 8325 by lepan last updated on 08/Oct/16 $${In}\:\Delta\:{ABC},\angle{A}=\mathrm{90}°\:,\:{AD}\bot{BC},\:{DE}\bot{AC}, \\ $$$${AF}\bot{FG},{GH}\bot{FC}. \\ $$$$\left({a}\right){How}\:{many}\:{triangles}\:{are}\:{there}? \\ $$$$\left({b}\right){If}\:{AB}=\frac{\mathrm{16}}{\mathrm{9}}\:,\:\angle{B}=\mathrm{60}°,{find}\:{the}\:{length} \\ $$$$\:\:\:\:\:\:{of}\:{GH}. \\ $$ Terms of Service Privacy Policy…
Question Number 139393 by BHOOPENDRA last updated on 26/Apr/21 Answered by Ar Brandon last updated on 26/Apr/21 $$\mathrm{I}=\int\frac{\mathrm{cos}{x}}{\mathrm{2cos}{x}+\mathrm{sin}{x}+\mathrm{3}}{dx},\:{t}=\mathrm{tan}\frac{{x}}{\mathrm{2}}\Rightarrow{dt}=\frac{\mathrm{1}+{t}^{\mathrm{2}} }{\mathrm{2}}{dx} \\ $$$$\:\:=\int\frac{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{2}\left(\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }\right)+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…