Question Number 64018 by Rio Michael last updated on 12/Jul/19 $${sin}\mathrm{3}\theta=? \\ $$$${cos}\mathrm{3}\theta=? \\ $$$${tan}\mathrm{3}\theta=? \\ $$ Commented by kaivan.ahmadi last updated on 12/Jul/19 $${sin}\mathrm{3}\theta={sin}\left(\mathrm{2}\theta+\theta\right)={sin}\mathrm{2}\theta{cos}\theta+{cos}\mathrm{2}\theta{sin}\theta=…
Question Number 64017 by Rio Michael last updated on 12/Jul/19 $${why}\:{can}'{t}\:{we}\:{differentiate}\:{or}\:{intergrate}\:{powers}\:{of}\:{trigonometric} \\ $$$${functions}\:{such}\:{as}\: \\ $$$$\left.\mathrm{1}\left.\right)\:\int{cos}^{\mathrm{2}} {xdx}?\:\:\:\:\mathrm{3}\right)\:\int{tan}^{\mathrm{2}} \mathrm{2}{xdx} \\ $$$$\left.\mathrm{2}\left.\right)\int{sin}^{\mathrm{2}} {xdx}?\:\:\:\:\:\mathrm{4}\right)\:\int{sin}^{\mathrm{10}} {x} \\ $$$${hence}\:{how}\:{do}\:{we}\:{solve}\:{such}\:{problems}.? \\ $$…
Question Number 64015 by Rio Michael last updated on 12/Jul/19 $$\:{How}\:{can}\:{such}\:{questions}\:{be}\:{solved}.? \\ $$$$\:\:{x}^{\mathrm{2}} −\mid\mathrm{7}\mid\:+\mathrm{10}=\mathrm{0} \\ $$$$\:\:{x}^{\mathrm{2}} −\mid{x}\mid−\mathrm{6}>\mathrm{0} \\ $$$$\:\: \\ $$ Answered by MJS last…
Question Number 64012 by aditya@345 last updated on 12/Jul/19 Answered by MJS last updated on 12/Jul/19 $$\begin{vmatrix}{\mathrm{3}}&{−\mathrm{2}}&{\mathrm{sin}\:\mathrm{3}\theta}\\{−\mathrm{7}}&{\mathrm{8}}&{\mathrm{cos}\:\mathrm{2}\theta}\\{−\mathrm{11}}&{\mathrm{14}}&{\mathrm{2}}\end{vmatrix}=\mathrm{0} \\ $$$$\mathrm{20}−\mathrm{20cos}\:\mathrm{2}\theta\:−\mathrm{10sin}\:\mathrm{3}\theta\:=\mathrm{0} \\ $$$$\mathrm{2cos}\:\mathrm{2}\theta\:+\mathrm{sin}\:\mathrm{3}\theta\:−\mathrm{2}=\mathrm{0} \\ $$$$\left(\mathrm{1}−\mathrm{2sin}\:\theta\right)\left(\mathrm{3}+\mathrm{2sin}\:\theta\right)\mathrm{sin}\:\theta\:=\mathrm{0} \\ $$$$\mathrm{sin}\:\theta\:=−\frac{\mathrm{3}}{\mathrm{2}}\:\Rightarrow\:\theta\notin\mathbb{R}…
Question Number 64011 by Prithwish sen last updated on 12/Jul/19 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{x}^{\mathrm{x}} −\mathrm{1}}{\mathrm{xlnx}} \\ $$ Commented by kaivan.ahmadi last updated on 12/Jul/19 $${y}={x}^{{x}} \Rightarrow{lny}={xlnx}\Rightarrow\frac{{y}'}{{y}}={lnx}+{x}×\frac{\mathrm{1}}{{x}}=\mathrm{1}+{lnx}\Rightarrow \\…
Question Number 129547 by Adel last updated on 16/Jan/21 $$\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{conditions}\:\mathrm{is}\:\mathrm{true}\: \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{folowing}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{verticale} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{a}_{\mathrm{1}} \mathrm{x}+\mathrm{b}_{\mathrm{1}} \mathrm{y}+\mathrm{c}_{\mathrm{1}} =\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{a}_{\mathrm{2}}…
Question Number 64009 by ajfour last updated on 12/Jul/19 Commented by ajfour last updated on 12/Jul/19 $${Find}\:{R}\:{in}\:{terms}\:{of}\:{a}\:{and}\:{b}. \\ $$ Answered by mr W last updated…
Question Number 129545 by mnjuly1970 last updated on 16/Jan/21 Answered by mindispower last updated on 16/Jan/21 $$=\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }−\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}…
Question Number 129542 by mr W last updated on 16/Jan/21 Commented by mr W last updated on 16/Jan/21 $${when}\:{the}\:{man}\:{climbs}\:{the}\:{ladder}\:{from} \\ $$$${bottom}\:{to}\:{top},\:{how}\:{much}\:{does}\:{the} \\ $$$${block}\:{move}\:{and}\:{in}\:{which}\:{direction}? \\ $$…
Question Number 129527 by MathSh last updated on 16/Jan/21 $${f}\left({x}\right)=\begin{cases}{\mathrm{5}−{x}\:;\:{x}\geqslant\mathrm{2}}\\{{x}^{\mathrm{2}} +\mathrm{3}\:;\:{x}<\mathrm{2}}\end{cases}\:\:\:{if}, \\ $$$${find}:\:{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{0}\right)=? \\ $$ Commented by bramlexs22 last updated on 16/Jan/21 $$=\:\mathrm{3}\:+\:\mathrm{3}\:=\:\mathrm{6} \\ $$…