Question Number 10750 by Joel576 last updated on 24/Feb/17 $$\mathrm{Exact}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{sin}\:\mathrm{9}°\:=\:… \\ $$ Answered by ridwan balatif last updated on 24/Feb/17 $$\mathrm{first}\:\mathrm{we}\:\mathrm{must}\:\mathrm{know}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{18}^{\mathrm{o}} \\ $$$$\mathrm{let}\:\mathrm{x}=\mathrm{18}^{\mathrm{o}}…
Question Number 141822 by mathsuji last updated on 23/May/21 Commented by MJS_new last updated on 23/May/21 $$\mathrm{where}\:\mathrm{you}\:\mathrm{found}\:\mathrm{this}? \\ $$$$\mathrm{did}\:\mathrm{your}\:\mathrm{teacher}\:\mathrm{gave}\:\mathrm{it}\:\mathrm{to}\:\mathrm{you}?\:\mathrm{which}\:\mathrm{chapter} \\ $$$$\mathrm{of}\:\mathrm{solving}\:\mathrm{equations}\:\mathrm{are}\:\mathrm{you}\:\mathrm{studying}? \\ $$$$\mathrm{have}\:\mathrm{you}\:\mathrm{got}\:\mathrm{any}\:\mathrm{idea}? \\ $$$$\bullet\:\mathrm{yes}:\:\mathrm{then}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{us}…
Question Number 10746 by okhema last updated on 24/Feb/17 $$\left.{i}\right){express}\:{the}\:{function}\:{f}\left(\theta\right)={sin}\theta\:+\:{cos}\theta\:{in}\:{the}\:{form}\:{rsin}\left(\theta+\alpha\right),\:{r}>\mathrm{0}\:{and}\:\mathrm{0}\leqslant\theta\leqslant\leqslant\frac{\pi}{\mathrm{2}} \\ $$$$\left.{ii}\right){hence}\:{find}\:{the}\:{maximum}\:{value}\:{of}\:{f}\:{and} \\ $$$${the}\:{smallest}\:{non}−{negative}\:{value}\:{of}\:\theta\:{at}\:{which}\:{it}\:{occurs}. \\ $$ Answered by mrW1 last updated on 24/Feb/17 $$\left.{i}\right) \\…
Question Number 10744 by okhema last updated on 24/Feb/17 $${hence}\:{or}\:{otherwise},{solve}\:{the}\:{equation}\:\frac{\mathrm{cosec}\:\theta}{\mathrm{cosec}\:\theta−\mathrm{sin}\:\theta}=\frac{\mathrm{4}}{\mathrm{3}}\:{for}\:\mathrm{0}\leqslant\theta\leqslant\mathrm{2}\Pi \\ $$ Answered by malwaan last updated on 24/Feb/17 $${cox}\:\theta=\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\Rightarrow\theta=\mathrm{30}°\:\:\boldsymbol{{or}}\:\boldsymbol{\theta}=\mathrm{180}−\mathrm{30}=\mathrm{150}° \\ $$$${or}\:\theta=\mathrm{180}+\mathrm{30}=\mathrm{210}°\:{or}\:\theta=−\mathrm{30}° \\…
Question Number 10743 by okhema last updated on 24/Feb/17 $${show}\:{that}\:\mathrm{sec}\:^{\mathrm{2}} \theta=\frac{\mathrm{cosec}\:\theta}{\mathrm{cosec}\:\theta−\mathrm{sin}\:} \\ $$ Commented by ridwan balatif last updated on 24/Feb/17 $$\frac{\mathrm{cosec}\theta}{\mathrm{cosec}\theta−\mathrm{sin}\theta}=\frac{\frac{\mathrm{1}}{\mathrm{sin}\theta}}{\frac{\mathrm{1}}{\mathrm{sin}\theta}−\mathrm{sin}\theta}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\frac{\mathrm{1}}{\mathrm{sin}\theta}}{\frac{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \theta}{\mathrm{sin}\theta}}…
Question Number 141812 by mathsuji last updated on 23/May/21 Commented by mr W last updated on 23/May/21 $${check}\:{your}\:{question}\:{and}\:{diagram}! \\ $$$$\angle{BEC}=\alpha\:? \\ $$$${but}\:{according}\:{to}\:{diagram} \\ $$$$\angle{BEC}=\mathrm{180}° \\…
Question Number 10742 by okhema last updated on 24/Feb/17 $${let}\:{the}\:{roots}\:{of}\:{the}\:{equation}\mathrm{2}{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{6}=\mathrm{0} \\ $$$${be}\:\alpha,\beta\:{and}\:\gamma. \\ $$$$\left.{i}\right){state}\:{the}\:{values}\:{of}\:\alpha+\beta+\gamma,\:\alpha\beta+\alpha\gamma+\beta\gamma\:{and}\:\alpha\beta\gamma. \\ $$$$\left.{ii}\right){hence}\:{or}\:{otherwise}\:{determine}\:{an}\:{equation}\:{with}\:{integer}\:{coefficients}\:{which}\:{as}\:{roots}\:\frac{\mathrm{1}}{\alpha^{\mathrm{2}\:} },\:\frac{\mathrm{1}}{\beta^{\mathrm{2}} }\:,\:{and}\:\frac{\mathrm{1}}{\gamma^{\mathrm{2}} } \\ $$$$ \\ $$…
Question Number 10741 by okhema last updated on 24/Feb/17 $${a}\:{function}\:{f}\:{is}\:{defined}\:{by}\:{f}\left({x}\right)=\:\frac{{x}+\mathrm{3}}{{x}−\mathrm{1}},\:{x}\:{not}\:{equal}\:{to}\:\mathrm{1}.{determine}\:{whether}\:{f}\:{is}\:{bijective},{that}\:{is},{both}\:{one}\:{to}\:{one}\:{and}\:{onto} \\ $$$$ \\ $$ Answered by mrW1 last updated on 24/Feb/17 $${f}\left({x}\right)=\:\frac{{x}+\mathrm{3}}{{x}−\mathrm{1}}={y} \\ $$$${x}+\mathrm{3}={yx}−{y} \\…
Question Number 141814 by gsk2684 last updated on 12/Jul/21 $${please}\:{help}\:{me}\:{finding}\:{the}\:{roots}\:{of}\:\: \\ $$$${x}^{\mathrm{5}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{20}{x}^{\mathrm{3}} +\mathrm{60}{x}^{\mathrm{2}} +\mathrm{120}{x}+\mathrm{120}=\mathrm{0}? \\ $$ Commented by MJS_new last updated on 23/May/21…
Question Number 76277 by TawaTawa last updated on 25/Dec/19 Answered by MJS last updated on 25/Dec/19 $$\left(\mathrm{1}\right)\:\Rightarrow\:{y}=\mathrm{4}−\mathrm{2}{x} \\ $$$$\Rightarrow \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{4}\left(\mathrm{4}−{x}\right)^{\mathrm{4}−{x}} ={x}\left(\mathrm{4}−\mathrm{2}{x}\right)^{\mathrm{2}} \mathrm{3}^{\mathrm{4}−{x}} \\ $$$$\mathrm{let}\:{t}=\mathrm{4}−{x}\:\Leftrightarrow\:{x}=\mathrm{4}−{t}…