Question Number 196639 by bbbbbbbb last updated on 29/Aug/23 $$\mathrm{if}\:\mathrm{sinx}=\frac{\mathrm{2}}{\mathrm{3}}\:\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{sin}}^{\mathrm{6}} \boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{cos}}^{\mathrm{6}} \boldsymbol{\mathrm{x}}??? \\ $$ Answered by AST last updated on 28/Aug/23 $$=\left({sin}^{\mathrm{2}} {x}+{cos}^{\mathrm{2}} {x}\right)^{\mathrm{3}} −\mathrm{3}{sin}^{\mathrm{2}}…
Question Number 196633 by mathexperience last updated on 28/Aug/23 Commented by mathexperience last updated on 28/Aug/23 $$\mathrm{8} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 196629 by universe last updated on 28/Aug/23 $${if}\:{xyz}=\mathrm{1},\:{prove} \\ $$$$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{y}}{{y}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{z}}{{z}−\mathrm{1}}\right)^{\mathrm{2}} \geqslant\mathrm{1}. \\ $$ Commented by universe last updated on 28/Aug/23 $$…
Question Number 196612 by Calculusboy last updated on 28/Aug/23 Commented by Frix last updated on 28/Aug/23 $$\mathrm{Question}\:\mathrm{196165} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 196614 by mr W last updated on 28/Aug/23 $${if}\:{S}_{{n}} =\frac{\mathrm{1}}{\mathrm{1}+\mathrm{5}{n}}+\frac{\mathrm{1}}{\mathrm{2}+\mathrm{5}{n}}+\frac{\mathrm{1}}{\mathrm{3}+\mathrm{5}{n}}+…+\frac{\mathrm{1}}{\mathrm{6}{n}}, \\ $$$${find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{S}_{{n}} =? \\ $$ Answered by universe last updated on 28/Aug/23…
Question Number 196582 by MATHEMATICSAM last updated on 27/Aug/23 $$\mathrm{If}\:{x}\:=\:\mathrm{log}_{{a}} {bc},\:{y}\:=\:\mathrm{log}_{{b}} {ca}\:\mathrm{and}\:{z}\:=\:\mathrm{log}_{{c}} {ab} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{x}\:+\:{y}\:+\:{z}\:=\:{xyz}\:−\:\mathrm{2}. \\ $$ Answered by som(math1967) last updated on 27/Aug/23 $${x}={log}_{{a}}…
Question Number 196555 by hardmath last updated on 27/Aug/23 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\Sigma\:\frac{\mathrm{1}\:+\:\mathrm{cos}\:\centerdot\:\left(\mathrm{A}\:−\:\mathrm{B}\right)\:\centerdot\:\mathrm{cos}\:\mathrm{C}}{\mathrm{h}_{\boldsymbol{\mathrm{C}}} \:\centerdot\:\mathrm{sec}\:\mathrm{C}}\:\:=\:\:\frac{\mathrm{3}}{\mathrm{2}\:\mathrm{R}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196544 by mr W last updated on 27/Aug/23 Answered by witcher3 last updated on 27/Aug/23 $$\mathrm{f}\left(\mathrm{k}+\mathrm{1}\right)=\mathrm{f}\left(\mathrm{1}\right)+\mathrm{f}\left(\mathrm{k}\right)+\mathrm{k} \\ $$$$\Rightarrow\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\left(\mathrm{f}\left(\mathrm{k}+\mathrm{1}\right)−\mathrm{f}\left(\mathrm{k}\right)\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\mathrm{f}\left(\mathrm{1}\right)+\mathrm{k}=\left(\mathrm{n}−\mathrm{1}\right)\mathrm{f}\left(\mathrm{1}\right)+\frac{\mathrm{n}}{\mathrm{2}}\left(\mathrm{n}−\mathrm{1}\right) \\…
Question Number 196519 by mr W last updated on 26/Aug/23 $${if}\:{xyz}=\mathrm{1},\:{prove} \\ $$$$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{y}}{{y}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{z}}{{z}−\mathrm{1}}\right)^{\mathrm{2}} \geqslant\mathrm{1}. \\ $$ Answered by mahdipoor last updated on 27/Aug/23…
Question Number 196515 by hardmath last updated on 26/Aug/23 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:+\infty} \:\mathrm{x}^{\boldsymbol{\pi}} \:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$ Answered by aleks041103 last updated on 26/Aug/23 $$\int_{\mathrm{0}} ^{\infty}…