Question Number 59177 by 2772639291927 last updated on 05/May/19 $$\int\:\:\frac{\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{cos}\:{x}}\:{dx}\:= \\ $$ Commented by mathsolverby Abdo last updated on 05/May/19 $${I}\:=\int\frac{\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}}{{cosx}}{dx}\:=\int\mathrm{2}{cosx}\:{dx}−\int\frac{{dx}}{{cosx}} \\ $$$${but}\:\int\:\mathrm{2}{cosxdx}\:=\mathrm{2}{sinx}\:+{c}_{\mathrm{1}} \\…
Question Number 59170 by 2772639291927 last updated on 05/May/19 $$\mathrm{If}{f}\left({x}\right)=\begin{vmatrix}{\mathrm{sec}\:{x}}&{\mathrm{cos}\:{x}}&{\mathrm{sec}^{\mathrm{2}} {x}+\mathrm{cosec}\:{x}\:\mathrm{cot}\:{x}}\\{\mathrm{cos}^{\mathrm{2}} {x}}&{\mathrm{cos}^{\mathrm{2}} {x}}&{\:\:\:\:\:\:\:\:\:\:\mathrm{cosec}^{\mathrm{2}} {x}}\\{\:\:\:\mathrm{1}}&{\mathrm{cos}^{\mathrm{2}} {x}}&{\:\:\:\:\:\:\:\:\:\:\mathrm{cos}^{\mathrm{2}} {x}}\end{vmatrix} \\ $$$$\mathrm{then}\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\left({x}\right)\:{dx}\:= \\ $$ Answered by MJS…
Question Number 59049 by ugwu Kingsley last updated on 03/May/19 $$\:\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}\:\mathrm{log}\:{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 58211 by salaw2000 last updated on 20/Apr/19 $$\underset{\:\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\:\mid\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:\mid{dx}\:= \\ $$ Commented by tanmay last updated on 20/Apr/19 Commented by tanmay last…
Question Number 58177 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{2}\:\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\:\:= \\ $$ Answered by math1967 last updated on 19/Apr/19 $$\frac{\pi}{\mathrm{3}}+\mathrm{2}×\frac{\pi}{\mathrm{6}}=\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$…
Question Number 58176 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{If}\:\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} ,\:{x}_{\mathrm{4}} \:\:\mathrm{are}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{4}} −{x}^{\mathrm{3}} \mathrm{sin}\:\mathrm{2}\beta+{x}^{\mathrm{2}} \mathrm{cos}\:\mathrm{2}\beta−{x}\:\mathrm{cos}\:\beta−\mathrm{sin}\:\beta=\mathrm{0}, \\ $$$$\mathrm{then} \\ $$$$\mathrm{tan}^{−\mathrm{1}} {x}_{\mathrm{1}}…
Question Number 58175 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\left(\pi+\theta\right)\:\mathrm{sin}\left(\pi−\theta\right)\:\mathrm{cosec}^{\mathrm{2}} \theta \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by math1967 last updated on 19/Apr/19 $$−{sin}\theta×{sin}\theta×{cosec}^{\mathrm{2}} \theta=−\mathrm{1}…
Question Number 58174 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{Four}\:\mathrm{digit}\:\mathrm{integers}\:\mathrm{are}\:\mathrm{taken}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{and}\:\mathrm{are}\:\mathrm{multiplied}\:\mathrm{together}.\:\mathrm{Then}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{them}\:\mathrm{will} \\ $$$$\mathrm{be}\:\mathrm{alive}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{year}\:\mathrm{is} \\ $$ Commented by mr W last updated…
Question Number 58056 by Salomon M. last updated on 17/Apr/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{forces}\:\mathrm{2}\boldsymbol{\mathrm{i}}−\mathrm{5}\boldsymbol{\mathrm{j}}+\mathrm{6}\boldsymbol{\mathrm{k}}\:\mathrm{and} \\ $$$$−\boldsymbol{\mathrm{i}}+\mathrm{2}\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}}\:\mathrm{act}\:\mathrm{on}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{due}\:\mathrm{to}\:\mathrm{which} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{displaced}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:{A}\left(\mathrm{4},−\mathrm{3},−\mathrm{2}\right) \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{point}\:{B}\left(\mathrm{6},\:\mathrm{1},−\mathrm{3}\right),\:\mathrm{then}\:\mathrm{the}\:\mathrm{work}\: \\ $$$$\mathrm{done}\:\mathrm{by}\:\mathrm{the}\:\mathrm{forces}\:\mathrm{is} \\ $$ Answered by tanmay last…
Question Number 58055 by Salomon M. last updated on 17/Apr/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{forces}\:\mathrm{2}\boldsymbol{\mathrm{i}}−\mathrm{5}\boldsymbol{\mathrm{j}}+\mathrm{6}\boldsymbol{\mathrm{k}}\:\mathrm{and} \\ $$$$−\boldsymbol{\mathrm{i}}+\mathrm{2}\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}}\:\mathrm{act}\:\mathrm{on}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{due}\:\mathrm{to}\:\mathrm{which} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{displaced}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:{A}\left(\mathrm{4},−\mathrm{3},−\mathrm{2}\right) \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{point}\:{B}\left(\mathrm{6},\:\mathrm{1},−\mathrm{3}\right),\:\mathrm{then}\:\mathrm{the}\:\mathrm{work}\: \\ $$$$\mathrm{done}\:\mathrm{by}\:\mathrm{the}\:\mathrm{forces}\:\mathrm{is} \\ $$ Answered by Kunal12588 last…