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) \\…
Question Number 164675 by amin96 last updated on 20/Jan/22 Commented by mr W last updated on 20/Jan/22 $${you}\:{meant}\:\geqslant\mathrm{1994}\:? \\ $$ Commented by amin96 last updated…
Question Number 164606 by cortano1 last updated on 19/Jan/22 $$\:{Min}\:{f}\left({x}\right)=\:\mathrm{cos}\:\mathrm{2}{x}\:+\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{2}{x}\:−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{cos}\:{x}−\mathrm{2sin}\:{x} \\ $$$$\:{is}\:… \\ $$ Answered by bobhans last updated on 19/Jan/22 $$\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{cos}\:\mathrm{2x}\:+\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{2x}\:−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{x}−\mathrm{2sin}\:\mathrm{x}\: \\ $$$$\:\mathrm{set}\:\vartheta\:=\mathrm{sin}\:\mathrm{x}+\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{x}\Rightarrow\vartheta^{\mathrm{2}} \:=\mathrm{sin}\:^{\mathrm{2}}…
Question Number 164599 by mathlove last updated on 19/Jan/22 $$\mathrm{180}<\theta<\mathrm{270}\:\:\:\:{and} \\ $$$$\mathrm{2}{sin}\theta−\mathrm{cos}\:\theta=\mathrm{0} \\ $$$${faind}\:\:\:{volue}\:{of} \\ $$$$\mathrm{sin}\:\theta×\mathrm{cos}\:\theta=? \\ $$ Commented by cortano1 last updated on 19/Jan/22…