Question Number 108573 by mnjuly1970 last updated on 17/Aug/20 $$\:\:\:\:\:\:\:\:\:\mathrm{please}:\:\:\:\mathrm{in}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\:\frac{{cos}\left(\mathrm{A}\right)}{{sin}\left(\mathrm{B}\right){sin}\left(\mathrm{C}\right)}\:+\frac{{cos}\left(\mathrm{B}\right)}{{sin}\left(\mathrm{A}\right){sin}\left(\mathrm{C}\right)}+\frac{{cos}\left(\mathrm{C}\right)}{{sin}\left(\mathrm{A}\right){sin}\left(\mathrm{B}\right)}\:=\mathrm{2}\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by veth last updated on…
Question Number 174096 by mnjuly1970 last updated on 24/Jul/22 $$ \\ $$$$\:\:\:{f}\left({x}\right)=\:{ax}^{\:\mathrm{2}} +\:{bx}\:+{c}\:\:{is}\:{given} \\ $$$$\:\:\:\:\:\:{a}\:\neq\:{b}\:\neq\:{c}\:\:,\:{a}\:,\:{b}\:,\:{c}\:\in\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\:{a}\neq\mathrm{0}\:\:\:{and}\:\:\:: \\ $$$$\:\:\:\:\:\:\:\:{f}\left({ax}\:+\:{b}\:\right)={f}\:\left({bx}\:+\:{c}\right) \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({f}\left({b}\right)\:\:−\:{f}\left({a}\:\right)\right)=? \\ $$ Answered by…
Question Number 43027 by Raj Singh last updated on 06/Sep/18 Commented by math khazana by abdo last updated on 07/Sep/18 $${let}\:{I}\:=\:\int\:\:\:\frac{{x}^{\mathrm{2}} \:+\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)}{dx}\:{let}\:{decompose} \\ $$$${F}\left({x}\right)=\frac{{x}^{\mathrm{2}}…
Question Number 43008 by MJS last updated on 06/Sep/18 $$\left({y}'\right)^{\mathrm{2}} =−\mathrm{1}+\mathrm{sin}\:{x} \\ $$$${y}=? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $$\frac{{dy}}{{dx}}=\sqrt{−\mathrm{1}+{sinx}}\: \\ $$$$\frac{{dy}}{{dx}}=\sqrt{−\mathrm{1}\left(\mathrm{1}−{sinx}\right)}\:…
Question Number 42994 by MJS last updated on 06/Sep/18 $$\int\sqrt{\mathrm{1}+\frac{\mathrm{cos}\:{x}}{\mathrm{4tan}\:{x}}}{dx}=? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $${this}\:{problem}\:{snatched}\:{the}\:{sleep}\:{and}\:{mind}\:{hovering} \\ $$$${to}\:{get}\:{the}\:{answer}… \\ $$ Commented…
Question Number 108507 by Eric002 last updated on 17/Aug/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \sqrt{\frac{\mathrm{3}{cos}\mathrm{2}{x}−\mathrm{1}}{{cos}^{\mathrm{2}} \left({x}\right)}}\:{dx} \\ $$ Answered by Sarah85 last updated on 18/Aug/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{6}}} {\int}}\sqrt{\frac{\mathrm{3cos}\:\mathrm{2}{x}\:−\mathrm{1}}{\mathrm{cos}^{\mathrm{2}}…
Question Number 108506 by mnjuly1970 last updated on 17/Aug/20 Answered by mathmax by abdo last updated on 17/Aug/20 $$\mathrm{A}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)}\mathrm{dx}\:\Rightarrow\mathrm{A}\:=_{\mathrm{x}=\sqrt{\mathrm{3}}\mathrm{t}} \:\:\:\int_{\mathrm{0}}…
Question Number 108502 by mnjuly1970 last updated on 17/Aug/20 Commented by mnjuly1970 last updated on 17/Aug/20 $$\clubsuit{please}\:{prove}\:\:{above}\:{integrals} \\ $$$${equalities}.\clubsuit \\ $$ Answered by mathmax by…
Question Number 174024 by Michaelfaraday last updated on 23/Jul/22 Answered by behi834171 last updated on 23/Jul/22 $$\frac{\mathrm{1}}{\left({a}^{\mathrm{2}} +{t}^{\mathrm{2}} \right)\left({b}^{\mathrm{2}} +{t}^{\mathrm{2}} \right)}=\frac{\mathrm{1}}{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }.\frac{\left({a}^{\mathrm{2}} +{t}^{\mathrm{2}} \right)−\left({b}^{\mathrm{2}}…
Question Number 42945 by ajfour last updated on 05/Sep/18 $$\int_{\mathrm{0}} ^{\:\:\pi/\mathrm{2}} \frac{{dx}}{\:\sqrt{\mathrm{sin}\:{x}}}\:=\:? \\ $$ Commented by MJS last updated on 05/Sep/18 $$\mathrm{this}\:\mathrm{can}'\mathrm{t}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{with}\:\mathrm{elementar}\:\mathrm{methods}, \\ $$$$\mathrm{it}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{an}\:\mathrm{elliptic}\:\mathrm{integral},\:\mathrm{you}\:\mathrm{can}\:\mathrm{find} \\…