Question Number 17420 by sushmitak last updated on 05/Jul/17 $$\mathrm{tan}^{\mathrm{6}} \frac{\pi}{\mathrm{9}}−\mathrm{33tan}^{\mathrm{4}} \frac{\pi}{\mathrm{9}}+\mathrm{27tan}^{\mathrm{2}} \frac{\pi}{\mathrm{9}}=? \\ $$ Answered by Tinkutara last updated on 05/Jul/17 $$\mathrm{tan}\:\mathrm{3}\left(\frac{\pi}{\mathrm{9}}\right)\:=\:\sqrt{\mathrm{3}} \\ $$$$\sqrt{\mathrm{3}}\:=\:\frac{\mathrm{3}\:\mathrm{tan}\:\frac{\pi}{\mathrm{9}}\:−\:\mathrm{tan}^{\mathrm{3}}…
Question Number 148489 by bramlexs22 last updated on 28/Jul/21 Answered by liberty last updated on 28/Jul/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 82954 by john santu last updated on 26/Feb/20 $$\int\:\frac{\mathrm{cos}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}{\mathrm{sin}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\: \\ $$ Commented by john santu last updated on 26/Feb/20 $$\mathrm{let}\:\mathrm{u}=\:\mathrm{cos}\:\mathrm{2x}\:\Rightarrow\:\mathrm{dx}\:=\:−\frac{\mathrm{du}}{\mathrm{2}\sqrt{\mathrm{1}−\mathrm{u}^{\mathrm{2}} }} \\ $$$$\Rightarrow\int\:\frac{\:\mathrm{2u}^{\mathrm{2}}…
Question Number 82952 by TawaTawa1 last updated on 26/Feb/20 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\mathrm{y}\:\:+\:\:\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{1}}\:\:\:\geqslant\:\:\mathrm{1}\:\:\:\:\:\mathrm{and}\:\:\:\:\mathrm{0}\:\:<\:\:\mathrm{y}\:\:−\:\:\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{1}}\:\:\leqslant\:\:\mathrm{1} \\ $$$$\mathrm{if}\:\:\mathrm{y}\:\:\geqslant\:\mathrm{1} \\ $$ Answered by MJS last updated on 26/Feb/20 $${t}^{\mathrm{2}} ={y}^{\mathrm{2}}…
Question Number 82953 by TawaTawa1 last updated on 26/Feb/20 $$\mathrm{verify}\:\mathrm{that}:\:\:\:\:\:\:\mathrm{cosh}.\mathrm{cosh}^{−\mathrm{1}} \left(\mathrm{y}\right)\:\:\:=\:\:\:\mathrm{y},\:\:\:\:\:\mathrm{if}\:\:\:\:\:\mathrm{y}\:\:\in\:\:\left(\mathrm{1},\:\:\:+\:\infty\right) \\ $$ Commented by mathmax by abdo last updated on 26/Feb/20 $${we}\:{have}\:{ch}^{−\mathrm{1}} \left({y}\right)={ln}\left({y}+\sqrt{{y}^{\mathrm{2}} −\mathrm{1}}\right)\:\Rightarrow…
Question Number 82950 by jagoll last updated on 26/Feb/20 $$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}\:−\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} }\:=\: \\ $$ Commented by mathmax by abdo last updated on 26/Feb/20…
Question Number 148483 by puissant last updated on 28/Jul/21 $$\mathrm{Soit}\:\mathrm{f}\:\mathrm{une}\:\mathrm{fonction}\:\mathrm{continu}\:\mathrm{sur}\:\mathbb{R} \\ $$$$\mathrm{et}\:\mathrm{non}\:\mathrm{identiquement}\:\mathrm{nulle}, \\ $$$$\forall\:\mathrm{x},\mathrm{x}'\in\mathbb{R},\:\mathrm{f}\left(\mathrm{x}−\mathrm{x}'\right)+\mathrm{f}\left(\mathrm{x}+\mathrm{x}'\right)=\mathrm{2f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{x}'\right) \\ $$$$\mathrm{montrer}\:\mathrm{que}: \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{et}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(−\mathrm{x}\right).. \\ $$ Answered by Olaf_Thorendsen last updated…
Question Number 82944 by jagoll last updated on 26/Feb/20 $$ \\ $$$$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{27}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{87}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{33}^{\mathrm{o}} \right)\:= \\ $$ Commented by john santu last…
Question Number 148482 by mathdanisur last updated on 28/Jul/21 Commented by hknkrc46 last updated on 28/Jul/21 $$\bigstar\:\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{2}}{\mathrm{79}}\:+\:\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{3} \\ $$$$=\:\left(\frac{\mathrm{1}}{\mathrm{78}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{2}}{\mathrm{79}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{1}\right) \\ $$$$=\:\frac{−\mathrm{77}}{\mathrm{78}}\:+\:\frac{−\mathrm{77}}{\mathrm{79}}\:+\:\frac{−\mathrm{77}}{\mathrm{80}} \\ $$$$=\:−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right) \\ $$$$\bigstar\:\frac{−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right)}{\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}}\:=\:−\mathrm{77}…
Question Number 17401 by ajfour last updated on 05/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{4}-\mathrm{digit}\:\mathrm{greatest} \\ $$$$\mathrm{number}\:\mathrm{and}\:\mathrm{the}\:\mathrm{5}-\mathrm{digit}\:\mathrm{smallest} \\ $$$$\mathrm{number},\:\mathrm{each}\:\mathrm{number}\:\mathrm{having}\:\mathrm{three} \\ $$$$\mathrm{different}\:\mathrm{digits}. \\ $$ Commented by RasheedSoomro last updated on 05/Jul/17…