Question Number 143898 by liberty last updated on 19/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78358 by aliesam last updated on 16/Jan/20 $${Q}.\:{solve} \\ $$$$ \\ $$$$\frac{\mathrm{2}^{{sin}^{\mathrm{2}} \left({x}\right)} }{{sin}^{\mathrm{2}} \left({x}\right)\:}\:+\:\frac{\mathrm{3}^{{cos}^{\mathrm{2}} \left({x}\right)} }{{cos}^{\mathrm{2}} \left({x}\right)}\:=\:\mathrm{6} \\ $$ Commented by MJS…
Question Number 143892 by mathmax by abdo last updated on 19/Jun/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}^{\mathrm{4}} \left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{4}} \:−\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy…
Question Number 12822 by fawadalamawan@gmail.com last updated on 02/May/17 $${prove}\:{by}\:{contradiction}\:\mathrm{9}+\mathrm{13}\sqrt{\mathrm{3}\:} \\ $$$${is}\:{irrational} \\ $$ Answered by mrW1 last updated on 03/May/17 $${let}\:{us}\:{assume}\:\mathrm{9}+\mathrm{13}\sqrt{\mathrm{3}}\:{is}\:{rational},.{i}.{e}. \\ $$$${there}\:{exist}\:{integer}\:{numbers}\:{a}\:{and}\:{b},\:{b}\neq\mathrm{0}, \\…
Question Number 78357 by TawaTawa last updated on 16/Jan/20 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\frac{\sqrt{\mathrm{1}\:+\:\mathrm{6x}}\:\:−\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:−\:\mathrm{6x}}}}{\:\sqrt{\mathrm{1}\:+\:\mathrm{3x}}\:\:−\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:−\:\mathrm{3x}}}}\:\:\:\:\:=\:\:\:\mathrm{4}\:+\:\mathrm{6x} \\ $$$$\mathrm{Ignoring}\:\mathrm{higher}\:\mathrm{power}\:\mathrm{of}\:\:\mathrm{x}\:\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$ Commented by MJS last updated on 16/Jan/20 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}\:\mathrm{this}\:\mathrm{question} \\ $$$$\mathrm{the}\:\mathrm{left}\:\mathrm{handed}\:\mathrm{side}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for} \\…
Question Number 143889 by mnjuly1970 last updated on 19/Jun/21 $$ \\ $$$$\:\:\:\:\:\:{A}\:\:{Challanging}\:\:{Integral}: \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{log}\left({x}\right).{log}\left(\mathrm{1}+{x}\right)}{\mathrm{1}−{x}}{dx} \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 78352 by Khyati last updated on 16/Jan/20 $${Find}\:\int\frac{\mathrm{1}}{{cos}^{\mathrm{2}} {x}\left(\mathrm{1}−{tanx}\right)^{\mathrm{2}} }\:{dx} \\ $$ Commented by jagoll last updated on 17/Jan/20 $$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} {x}\:{dx}}{\left(\mathrm{1}−\mathrm{tan}\:{x}\right)^{\mathrm{2}} }\:=\:−\int\:\frac{{d}\left(\mathrm{1}−\mathrm{tan}\:{x}\right)}{\left(\mathrm{1}−\mathrm{tan}\:{x}\right)^{\mathrm{2}} }…
Question Number 143890 by pandu last updated on 19/Jun/21 $${if}\:{a}+{b}+{c}=\pi\:\:\: \\ $$$$\:{tanA}+{tanB}+{tanC}\:={tanA}.{tanB}.{tanC} \\ $$$$\mathrm{FAILED}\:\mathrm{TO}\:\mathrm{CALCULATE} \\ $$ Answered by justtry last updated on 19/Jun/21 Answered by…
Question Number 78353 by TawaTawa last updated on 16/Jan/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78351 by loveineq. last updated on 16/Jan/20 $$\mathrm{Let}\:\:{a},{b},{c}\:\in\:\mathrm{R}^{+} \:\:\mathrm{and}\:\:\left({a}+{b}\right)\left({b}+{c}\right)\:=\:\mathrm{1}\:,\:\mathrm{where}\:\:\mathrm{0}\:<{b}\leqslant\:\mathrm{1}\:. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\:\mid{a}−{b}\mid\mid{b}−{c}\mid\:\geqslant\:\frac{\mid\sqrt{{a}}−\sqrt{{b}}\mid\mid\sqrt{{b}}−\sqrt{{c}}\mid}{\mathrm{2}}\:. \\ $$ Commented by loveineq. last updated on 19/Jan/20 $$\mathrm{More}\:\mathrm{stronger}\:\mathrm{is}\:\:\mid{a}−{b}\mid\mid{b}−{c}\mid\:\geqslant\:\mid\sqrt{{a}}−\sqrt{{b}}\mid\mid\sqrt{{b}}−\sqrt{{c}}\mid\:. \\ $$…