Question Number 18185 by Tinkutara last updated on 16/Jul/17 $$\mathrm{Is}\:\mathrm{this}\:\mathrm{true}\:\mathrm{or}\:\mathrm{false}? \\ $$$${a}\mathrm{cos}{A}\:+\:{b}\mathrm{cos}{B}\:+\:{c}\mathrm{cos}{C}\:=\:\frac{{abc}}{\mathrm{2}{R}^{\mathrm{2}} } \\ $$ Commented by b.e.h.i.8.3.417@gmail.com last updated on 16/Jul/17 $${yes}.\:{it}\:{is}\:{true}. \\ $$$${in}\:{triangle}\:{ABC},{draw}\:{altitudes}\:{of}…
Question Number 83721 by mr W last updated on 05/Mar/20 Commented by MJS last updated on 05/Mar/20 $$−\mathrm{3} \\ $$ Commented by john santu last…
Question Number 18184 by Tinkutara last updated on 16/Jul/17 $$\left({m}+\mathrm{2}\right)\mathrm{sin}\theta\:+\:\left(\mathrm{2}{m}−\mathrm{1}\right)\mathrm{cos}\theta\:=\:\mathrm{2}{m}+\mathrm{1},\:\mathrm{if} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{tan}\theta\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{tan}\theta\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{tan}\theta\:=\:\frac{\mathrm{2}{m}}{{m}^{\mathrm{2}} \:−\:\mathrm{1}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{tan}\theta\:=\:\frac{\mathrm{2}{m}}{{m}^{\mathrm{2}} \:+\:\mathrm{1}} \\ $$ Commented by prakash…
Question Number 149252 by holomata last updated on 04/Aug/21 $$ \\ $$$${e}^{{y}} =\left(\mathrm{sin}\:{x}\right)\left(\mathrm{cos}\:{x}\right) \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$ Answered by Mokmokhi last updated on 04/Aug/21 $$\frac{{dy}}{{dx}}=\mathrm{2cot}\:\mathrm{2}{x}…
Question Number 83719 by Roland Mbunwe last updated on 05/Mar/20 $${Question}.\:\:\:\:\:\:\:\:\overset{{Show}\:\:{that}\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \frac{{cosx}}{\mathrm{3}+{cos}^{\mathrm{2}} {x}}{dx}=\frac{\mathrm{1}}{\mathrm{4}}{ln}\mathrm{3}} {\:} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 83717 by M±th+et£s last updated on 05/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 149251 by john_santu last updated on 04/Aug/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{tan}\:\mathrm{x}}−\mathrm{sin}\:\mathrm{x}\:\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} \:\sqrt{\mathrm{x}}}\:=? \\ $$$$ \\ $$ Answered by dumitrel last updated on 04/Aug/21 $$\underset{{x}\rightarrow\mathrm{0}^{+}…
Question Number 83713 by mhmd last updated on 05/Mar/20 $$\int\frac{{dx}}{\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}\:\:\:{pleas}\:{sir}\:{help}\:{me} \\ $$ Commented by niroj last updated on 05/Mar/20 $$ \\ $$$$\:\:\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}}}}\mathrm{dx} \\ $$$$\:=\:\int\:\frac{\:\:\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{4x}+\mathrm{1}}}{\mathrm{2}}}\mathrm{dx}=\:\int\:\frac{\mathrm{2}}{\mathrm{1}+\sqrt{\mathrm{4x}+\mathrm{1}}}\mathrm{dx} \\…
Question Number 83710 by john santu last updated on 05/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}} }{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} }\:=\:? \\ $$ Commented by john santu last updated on…
Question Number 149244 by EDWIN88 last updated on 04/Aug/21 $$\:\:{Let}\:{a},{b},{c}\:{be}\:{positive}\:{real}\:{numbers} \\ $$$${with}\:{sum}\:\mathrm{3}.\:{Prove}\:{that}\: \\ $$$$\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}{a}^{\mathrm{2}} +{bc}}+\frac{\mathrm{3}}{\mathrm{2}{b}^{\mathrm{2}} +{ac}}+\frac{\mathrm{3}}{\mathrm{2}{c}^{\mathrm{2}} +{ab}} \\ $$ Terms of Service Privacy Policy Contact:…