Question Number 164912 by bobhans last updated on 23/Jan/22 $$\:\:\mathrm{If}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{9}\:,\:\mathrm{then}\:\mathrm{max}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\mathrm{x}+\mathrm{y}} \\ $$ Commented by bobhans last updated on 23/Jan/22 $$\mathrm{all}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{great} \\…
Question Number 164901 by cortano1 last updated on 23/Jan/22 Answered by bobhans last updated on 23/Jan/22 $$\:\Rightarrow\:\frac{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}\:−\frac{\mathrm{2}−\mathrm{3cos}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\:=\:\mathrm{0} \\ $$$$\Rightarrow\:\frac{\left(\mathrm{1}−\mathrm{c}\right)^{\mathrm{2}} }{\mathrm{c}^{\mathrm{2}} }\:−\frac{\mathrm{2}−\mathrm{3c}}{\mathrm{c}}\:=\:\mathrm{0}\:,\:\mathrm{c}\:=\:\mathrm{cos}\:^{\mathrm{2}}…
Question Number 99303 by Ar Brandon last updated on 20/Jun/20 Commented by Ar Brandon last updated on 20/Jun/20 I felt this could be helpful here. Especially when integrating with surds.�� Commented by MWSuSon last updated on…
Question Number 164820 by Avijit007 last updated on 22/Jan/22 Answered by Ar Brandon last updated on 22/Jan/22 $$\mathrm{Let}\:{x}\:\mathrm{and}\:{y}\:\mathrm{be}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\:{x}={e}^{{i}\vartheta} \:\mathrm{and}\:{y}={e}^{{i}\Phi} \\ $$$$\mathrm{Then}\:{x}^{{m}} +\frac{\mathrm{1}}{{x}^{{m}} }=\mathrm{2cos}\left({m}\vartheta\right)\:\mathrm{and}\:{y}^{{m}} +\frac{\mathrm{1}}{{y}^{{m}} }=\mathrm{2cos}\left({m}\Phi\right)…
Question Number 164808 by Mathematification last updated on 22/Jan/22 Answered by mr W last updated on 22/Jan/22 Commented by mr W last updated on 22/Jan/22…
Question Number 164760 by mathlove last updated on 21/Jan/22 $${tan}\mathrm{193}={k} \\ $$$${cos}\mathrm{167}=? \\ $$ Answered by blackmamba last updated on 21/Jan/22 $$\:\mathrm{tan}\:\left(\mathrm{193}°\right)=\mathrm{tan}\:\left(\mathrm{180}°+\mathrm{13}°\right)=\:{k}\: \\ $$$$\:\Rightarrow\mathrm{tan}\:\mathrm{13}°\:={k} \\…
Question Number 164757 by mathlove last updated on 21/Jan/22 $$\mathrm{cos}\:\alpha=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${sin}\left(\frac{\pi}{\mathrm{2}}+\alpha\right)−\mathrm{3}{sin}^{\mathrm{2}} \left(\frac{\mathrm{7}\pi}{\mathrm{2}}+\alpha\right)−\mathrm{2}{cos}\left(\mathrm{5}\pi+\alpha\right)=? \\ $$ Commented by blackmamba last updated on 21/Jan/22 $$\Rightarrow=\mathrm{cos}\:\alpha−\mathrm{3cos}\:^{\mathrm{2}} \alpha+\mathrm{2cos}\:\alpha \\…
Question Number 164758 by mathlove last updated on 21/Jan/22 $${tan}\mathrm{22}=\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\frac{{sin}\mathrm{112}+{sin}\mathrm{202}}{{cos}\left(−\mathrm{68}\right)}=? \\ $$ Answered by Rasheed.Sindhi last updated on 21/Jan/22 $$\frac{\mathrm{sin}\:\mathrm{112}+\mathrm{sin}\:\mathrm{202}}{\mathrm{cos}\:\left(−\mathrm{68}\right)} \\ $$$$=\frac{\mathrm{sin}\left(\mathrm{90}+\mathrm{22}\right)+\mathrm{sin}\left(\mathrm{180}+\mathrm{22}\right)}{\:\mathrm{cos}\left(\mathrm{22}−\mathrm{90}\right)} \\…
Question Number 164720 by mathlove last updated on 21/Jan/22 $${tan}\mathrm{3}{x}=\mathrm{5}{tanx} \\ $$$${x}=? \\ $$ Answered by leonhard77 last updated on 21/Jan/22 $$\:\mathrm{tan}\:\mathrm{3}{x}=\frac{\mathrm{3tan}\:{x}−\mathrm{tan}\:^{\mathrm{3}} {x}}{\mathrm{1}−\mathrm{3tan}\:^{\mathrm{2}} {x}}\:=\:\mathrm{5tan}\:{x} \\…
Question Number 164703 by amin96 last updated on 20/Jan/22 Answered by mr W last updated on 20/Jan/22 $$\underset{{n}=\mathrm{1}} {\overset{\mathrm{997}} {\sum}}\left(\mathrm{tan}^{\mathrm{2}} \:{x}_{{n}} +\frac{\mathrm{1}}{\mathrm{tan}^{\mathrm{2}} \:{x}_{{n}} }\right) \\…