Question Number 73538 by Rio Michael last updated on 13/Nov/19 $${find}\:{the}\:{general}\:{solution}\:{of}\: \\ $$$$\:{sin}\mathrm{4}{x}\:+\:{cos}\mathrm{2}{x}\:=\:\mathrm{0} \\ $$ Answered by ajfour last updated on 13/Nov/19 $$\mathrm{cos}\:\mathrm{2}{x}\left(\mathrm{2sin}\:\mathrm{2}{x}+\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow\:\:\mathrm{2}{x}=\left(\mathrm{2}{n}+\mathrm{1}\right)\frac{\pi}{\mathrm{2}}\:\:\:{or}…
Question Number 8003 by Yozzia last updated on 27/Sep/16 $$\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left(\underset{{r}=\mathrm{0}} {\overset{{m}−\mathrm{1}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}+\mathrm{1}}\end{pmatrix}\:\left(−\mathrm{1}\right)^{{m}−{r}} \right)^{\mathrm{2}} +\left(\underset{{r}=\mathrm{0}} {\overset{{m}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}}\end{pmatrix}\:\left(−\mathrm{1}\right)^{{m}−{r}} \right)^{\mathrm{2}} }\right)=? \\ $$ Commented by prakash…
Question Number 139075 by bramlexs22 last updated on 22/Apr/21 Answered by mr W last updated on 22/Apr/21 $$\mathrm{tan}\:\alpha=\frac{{x}}{\mathrm{144}} \\ $$$$\mathrm{tan}\:\beta=\frac{{x}}{\mathrm{144}+\mathrm{81}}=\frac{{x}}{\mathrm{225}} \\ $$$$\mathrm{tan}\:\gamma=\frac{{x}}{\mathrm{225}+\mathrm{99}}=\frac{{x}}{\mathrm{324}} \\ $$$$\mathrm{tan}\:\gamma=\mathrm{tan}\:\left(\mathrm{90}°−\alpha−\beta\right)=\frac{\mathrm{1}}{\mathrm{tan}\:\left(\alpha+\beta\right)} \\…
Question Number 73536 by Rio Michael last updated on 13/Nov/19 $${prove}\:{that}\:{they}\:{are}\:{infinitely}\:{many}\:{primes} \\ $$ Answered by MJS last updated on 13/Nov/19 $$\mathrm{if}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{primes}\:\mathrm{is}\:\mathrm{finite},\:\mathrm{number} \\ $$$$\mathrm{them}\:{p}_{\mathrm{1}} ,\:{p}_{\mathrm{2}} ,…{p}_{{n}}…
Question Number 73537 by Rio Michael last updated on 13/Nov/19 $${prove}\:{by}\:{induction}\:{that}\:\mathrm{4}^{{n}} \:+\:\mathrm{3}^{{n}} \:+\mathrm{2}\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{3} \\ $$$$\forall\:{n}\:{Z}^{+} \\ $$ Answered by mind is power last updated on…
Question Number 7999 by FilupSmith last updated on 27/Sep/16 $${S}=\frac{\mathrm{1}}{{n}}+\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{8}{n}^{\mathrm{8}} }+… \\ $$$${S}=\frac{\mathrm{1}}{{n}}+\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{{i}} {n}^{\mathrm{2}^{{i}} } } \\ $$$$\mathrm{Solvable}? \\ $$ Answered…
Question Number 7996 by ridwan balatif last updated on 27/Sep/16 $${how}\:{to}\:{prove}\:{this} \\ $$$$\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \mathrm{10}^{{o}} }+\frac{\mathrm{1}}{{sin}^{\mathrm{2}} \mathrm{20}^{{o}} }+\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \mathrm{40}}=\mathrm{12} \\ $$ Commented by prakash jain last…
Question Number 73530 by Rio Michael last updated on 13/Nov/19 $${given}\:{the}\:\mathrm{3}^{{rd}} \:{degree}\:\:{polynomial} \\ $$$${P}\left({x}\right)\:=\:\left(\mathrm{2}{x}\:−\mathrm{1}\right)\left({x}−\mathrm{3}\right){Q}\left({x}\right)\:+\:\mathrm{12}{x}−\mathrm{8} \\ $$$${given}\:{that}\:\left({x}−\mathrm{1}\right)\:{is}\:{a}\:{factor}\:{of}\:{P}\left({x}\right)\:{and}\:\:{P}\left(\mathrm{0}\right)\:=\:\mathrm{10} \\ $$$${find}\:{Q}\left({x}\right) \\ $$ Answered by MJS last updated…
Question Number 139060 by 0731619177 last updated on 21/Apr/21 Commented by Dwaipayan Shikari last updated on 21/Apr/21 $${There}\:{is}\:{no}\:{such}\:{thing}\:{as}\:{dark}.\: \\ $$ Commented by 0731619177 last updated…
Question Number 73525 by arkanmath7@gmail.com last updated on 13/Nov/19 Commented by mathmax by abdo last updated on 13/Nov/19 $${z}^{\mathrm{2}} +\left(\mathrm{1}−{i}\right){z}−\mathrm{3}{i}\:=\mathrm{0} \\ $$$$\Delta=\left(\mathrm{1}−{i}\right)^{\mathrm{2}} −\mathrm{4}\left(−\mathrm{3}{i}\right)\:=\mathrm{1}−\mathrm{2}{i}−\mathrm{1}+\mathrm{12}{i}\:=\mathrm{10}{i} \\ $$$${z}_{\mathrm{1}}…