Question Number 12078 by agni5 last updated on 12/Apr/17 $$\mathrm{If}\:\mathrm{tan}\:^{\mathrm{2}} \alpha\:=\:\mathrm{1}+\mathrm{2tan}\:^{\mathrm{2}} \beta\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\mathrm{cos}\:\mathrm{2}\beta\:=\mathrm{1}+\mathrm{2cos}\:\mathrm{2}\alpha\:. \\ $$ Answered by ajfour last updated on 12/Apr/17 $$\mathrm{1}+\mathrm{2cos}\:\mathrm{2}\alpha\:=\mathrm{1}+\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \alpha\right)}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}}…
Question Number 12077 by tawa last updated on 12/Apr/17 $$\mathrm{A}\:\mathrm{man}\:\mathrm{travels}\:\mathrm{29}\:\mathrm{km}\:\mathrm{on}\:\mathrm{an}\:\mathrm{open}\:\mathrm{road}\:\mathrm{at}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{speed}.\:\mathrm{In}\:\mathrm{the}\:\mathrm{city},\:\mathrm{he}\: \\ $$$$\mathrm{reduce}\:\mathrm{his}\:\mathrm{speed}\:\mathrm{by}\:\mathrm{420}\:\mathrm{km}/\mathrm{hr},\:\mathrm{and}\:\mathrm{he}\:\mathrm{find}\:\mathrm{that}\:\mathrm{he}\:\mathrm{take}\:\mathrm{him}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time} \\ $$$$\mathrm{to}\:\mathrm{cover}\:\mathrm{15}\:\mathrm{km},\:\mathrm{Find}\:\mathrm{his}\:\mathrm{average}\:\mathrm{speed}.\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{On}\:\mathrm{the}\:\mathrm{open}\:\mathrm{road} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{In}\:\mathrm{the}\:\mathrm{city} \\ $$ Answered by sandy_suhendra last updated…
Question Number 143150 by ZiYangLee last updated on 10/Jun/21 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\begin{vmatrix}{{x}−\mathrm{cos}\:\theta}&{−\mathrm{sin}\:\theta}\\{\mathrm{sin}\:\theta}&{{x}−\mathrm{cos}\:\theta}\end{vmatrix}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\alpha^{{n}} +\beta^{{n}} ,\:\mathrm{where}\:{n}\in\mathbb{N}. \\ $$ Commented by mr W last updated on…
Question Number 12074 by sin (x) last updated on 11/Apr/17 Answered by ajfour last updated on 11/Apr/17 Commented by ajfour last updated on 11/Apr/17 $${M}\:{is}\:{the}\:{mid}-{point}\:{of}\:{CD}.…
Question Number 143147 by mathmax by abdo last updated on 10/Jun/21 $$\mathrm{montrer}\:\mathrm{que}\:\mathrm{lasuite}\:\mathrm{U}_{\mathrm{n}} =\frac{\mathrm{H}_{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} }\:\mathrm{est}\:\mathrm{bornee} \\ $$$$\mathrm{H}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} } \\ $$ Commented by…
Question Number 77608 by aliesam last updated on 08/Jan/20 $$\int\frac{\left(\:{ln}\mid{tan}\left(\frac{{nx}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)\mid\:\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:\:;{n}>\mathrm{0}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 77607 by otchereabdullai@gmail.com last updated on 08/Jan/20 $$\mathrm{Two}\:\mathrm{bell}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{rings}\:\mathrm{in}\:\mathrm{different}\: \\ $$$$\mathrm{time}\:\mathrm{interval}.\:\mathrm{Bell}\:\mathrm{A}\:\mathrm{rings}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{interval}\:\mathrm{of}\:\mathrm{8minutes}\:\mathrm{while}\:\mathrm{Bell}\:\mathrm{B}\:\mathrm{rings} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{9minutes}.\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{bell}\:\mathrm{rings}\:\mathrm{together}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{time}\: \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{time}\:\mathrm{is}\:\mathrm{10}:\mathrm{00am} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{At}\:\mathrm{what}\:\mathrm{time}\:\mathrm{will}\:\mathrm{the}\:\mathrm{two}\:\mathrm{bell}\:\mathrm{ring} \\ $$$$\mathrm{together}\:\mathrm{again}. \\…
Question Number 77604 by jagoll last updated on 08/Jan/20 $${given} \\ $$$$\frac{\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right)}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}=−\frac{\mathrm{1}}{\mathrm{30}} \\ $$$${what}\:{the}\:{value}\:{of}\: \\ $$$$\frac{{b}}{{a}+{b}}+\frac{{c}}{{b}+{c}}+\frac{{a}}{{c}+{a}}\:? \\ $$ Answered by key of knowledge last updated…
Question Number 143142 by Ar Brandon last updated on 10/Jun/21 $$\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\centerdot\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }}\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 10/Jun/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}}…