Question Number 83036 by otchereabdullai@gmail.com last updated on 27/Feb/20 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{cos}^{\mathrm{4}} \theta−\mathrm{sin}^{\mathrm{4}} \theta=\mathrm{cos}^{\mathrm{2}} \theta−\mathrm{sin}^{\mathrm{2}} \theta \\ $$ Commented by Tony Lin last updated on 27/Feb/20 $${cos}^{\mathrm{4}}…
Question Number 83037 by otchereabdullai@gmail.com last updated on 27/Feb/20 $$\mathrm{If}\:\mathrm{m}=\frac{\mathrm{1}−\mathrm{cos}\theta}{\mathrm{sin}\theta}\:,\:\:\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{m}}=\:\frac{\mathrm{1}+\mathrm{sin}\theta}{\mathrm{sin}\theta} \\ $$ Commented by Tony Lin last updated on 27/Feb/20 $$\frac{\mathrm{1}}{{m}}=\frac{{sin}\theta}{\mathrm{1}−{cos}\theta}=\:\frac{{sin}\theta\left(\mathrm{1}+{cos}\theta\right)}{\left(\mathrm{1}−{cos}\theta\right)\left(\mathrm{1}+{cos}\theta\right)} \\ $$$$=\frac{\mathrm{1}+{cos}\theta}{{sin}\theta} \\ $$…
Question Number 148569 by puissant last updated on 29/Jul/21 Commented by Olaf_Thorendsen last updated on 29/Jul/21 $$\mathrm{Remarque}\:: \\ $$$$\mathrm{Si}\:{x}\:\mathrm{est}\:\mathrm{le}\:\mathrm{laps}\:\mathrm{de}\:\mathrm{temps}\:\mathrm{que}\:\mathrm{les}\:\mathrm{deux} \\ $$$$\mathrm{amis}\:\mathrm{acceptent}\:\mathrm{de}\:\mathrm{s}'\mathrm{attendre},\:\mathrm{la}\: \\ $$$$\mathrm{formule}\:\mathrm{generale}\:\mathrm{est}\:: \\ $$$${p}\:=\:\mathrm{1}−\frac{\left(\mathrm{60}−{x}\right)^{\mathrm{2}}…
Question Number 148568 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{sh}\left(\mathrm{2sinx}\right)−\mathrm{sin}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by Ar Brandon last updated on 29/Jul/21 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 83035 by bshahid010@gmail.com last updated on 27/Feb/20 Commented by Tony Lin last updated on 27/Feb/20 $${f}\left(\mathrm{1}\right)=\mathrm{4}{f}\left(\mathrm{0}\right)\Rightarrow{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${f}\left(\mathrm{2}\right)=\left(\sqrt{{f}\left(\mathrm{0}\right)}+\sqrt{{f}\left(\mathrm{1}\right)}\right)^{\mathrm{2}} \\ $$$$={f}\left(\mathrm{0}\right)+{f}\left(\mathrm{1}\right)+\mathrm{2}\sqrt{{f}\left(\mathrm{0}\right){f}\left(\mathrm{1}\right)} \\ $$$$=\frac{\mathrm{9}}{\mathrm{4}}{f}\left(\mathrm{1}\right)=\mathrm{9}{f}\left(\mathrm{0}\right)=\mathrm{9} \\…
Question Number 83032 by Power last updated on 27/Feb/20 Answered by mr W last updated on 27/Feb/20 Commented by mr W last updated on 27/Feb/20…
Question Number 17497 by tawa tawa last updated on 06/Jul/17 $$\mathrm{Evaluate}:\:\:\:\mathrm{sin}\left(\mathrm{9}\right)° \\ $$ Answered by mrW1 last updated on 06/Jul/17 $$\mathrm{18}°+\mathrm{2}×\mathrm{18}°=\mathrm{90}°−\mathrm{2}×\mathrm{18}° \\ $$$$\mathrm{cos}\:\left(\mathrm{18}°+\mathrm{2}×\mathrm{18}°\right)=\mathrm{cos}\:\left(\mathrm{90}°−\mathrm{2}×\mathrm{18}°\right)=\mathrm{sin}\:\left(\mathrm{2}×\mathrm{18}°\right) \\ $$$$\mathrm{cos}\:\mathrm{18}\:\mathrm{cos}\:\left(\mathrm{2}×\mathrm{18}\right)−\mathrm{sin}\:\mathrm{18}\:\mathrm{sin}\:\left(\mathrm{2}×\mathrm{18}\right)=\mathrm{sin}\:\left(\mathrm{2}×\mathrm{18}\right)…
Question Number 148570 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on 29/Jul/21…
Question Number 148565 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)} \\ $$ Answered by Ar Brandon last updated…
Question Number 83030 by Power last updated on 27/Feb/20 Answered by mr W last updated on 27/Feb/20 Commented by mr W last updated on 27/Feb/20…