Question Number 42410 by soufiane zarik last updated on 25/Aug/18 $$\underset{\:\mathrm{0}} {\overset{\mathrm{2}{a}} {\int}}\:\:\frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left(\mathrm{2}{a}−{x}\right)}\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 25/Aug/18 $${let}\:{A}\:=\:\int_{\mathrm{0}}…
Question Number 42345 by soufiane zarik last updated on 23/Aug/18 $$\mathrm{tan}\:\mathrm{15}°\:= \\ $$ Commented by MJS last updated on 24/Aug/18 $$\mathrm{tan}\:\mathrm{15}°\:=\mathrm{tan}\:\frac{\mathrm{30}°}{\mathrm{2}}\:=\frac{\mathrm{sin}\:\mathrm{30}°}{\mathrm{1}+\mathrm{cos}\:\mathrm{30}°}=\frac{\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}=\frac{\frac{\mathrm{1}}{\mathrm{2}}}{\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\mathrm{2}}}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{3}}}=\frac{\mathrm{2}−\sqrt{\mathrm{3}}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)}=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$…
Question Number 42094 by amansingh@123 last updated on 17/Aug/18 $$\mathrm{If}\:\:\mathrm{7}\:\mathrm{points}\:\mathrm{out}\:\mathrm{of}\:\:\mathrm{12}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{straight}\:\mathrm{line},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{triangles}\:\mathrm{formed}\:\mathrm{is} \\ $$ Answered by $@ty@m last updated on 17/Aug/18 $$\:^{\mathrm{7}} {C}_{\mathrm{2}}…
Question Number 42093 by amansingh@123 last updated on 17/Aug/18 $$\mathrm{If}\:\mathrm{the}\:\mathrm{permutations}\:\mathrm{of}\:{a},\:{b},\:{c},\:{d},\:{e}\:\mathrm{taken} \\ $$$$\mathrm{all}\:\mathrm{together}\:\mathrm{be}\:\mathrm{written}\:\mathrm{down}\:\mathrm{in}\: \\ $$$$\mathrm{alphabetical}\:\mathrm{order}\:\mathrm{as}\:\mathrm{in}\:\mathrm{dictionary} \\ $$$$\mathrm{and}\:\mathrm{numbered},\:\mathrm{then}\:\mathrm{the}\:\mathrm{rank}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{permutation}\:\:{debac}\:\:\mathrm{is} \\ $$ Answered by $@ty@m last updated…
Question Number 41896 by Ugguvj3 last updated on 15/Aug/18 $$\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\:\left[\:\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{\mathrm{2}} −\mathrm{2}\right]^{\mathrm{1}/\mathrm{2}} {dx}\:= \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 41820 by v tfvhjdxf last updated on 13/Aug/18 $$\mathrm{If}\:\alpha,\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{determinant} \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{cos}\:\left(\beta−\alpha\right)}&{\mathrm{cos}\:\alpha}\\{\mathrm{cos}\:\left(\alpha−\beta\right)}&{\mathrm{1}}&{\mathrm{cos}\:\beta}\\{\mathrm{cos}\:\alpha}&{\mathrm{cos}\:\beta}&{\mathrm{1}}\end{vmatrix}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 107330 by saorey0202 last updated on 10/Aug/20 $$\mathrm{If}\:\:\:{a}+{b}+{c}=\mathrm{0}\:\mathrm{one}\:\mathrm{root}\:\mathrm{of} \\ $$$$\begin{vmatrix}{{a}−{x}}&{\:\:\:\:{c}}&{\:\:\:{b}}\\{\:\:\:\:{c}}&{{b}−{x}}&{\:\:\:{a}}\\{\:\:\:\:{b}}&{\:\:\:{a}}&{{c}−{x}}\end{vmatrix}=\mathrm{0}\:\mathrm{is} \\ $$ Answered by som(math1967) last updated on 10/Aug/20 $$\begin{vmatrix}{\mathrm{a}+\mathrm{b}+\mathrm{c}−\mathrm{x}}&{\mathrm{a}+\mathrm{b}+\mathrm{c}−\mathrm{x}}&{\mathrm{a}+\mathrm{b}+\mathrm{c}−\mathrm{x}}\\{\mathrm{c}}&{\mathrm{b}−\mathrm{x}}&{\mathrm{a}}\\{\mathrm{b}}&{\mathrm{a}}&{\mathrm{c}−\mathrm{x}}\end{vmatrix}=\mathrm{0} \\ $$$$\left[\mathrm{R}_{\mathrm{1}} ^{'}…
Question Number 107331 by saorey0202 last updated on 10/Aug/20 $$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{an}\:\mathrm{invertible}\:\mathrm{matrix},\:\mathrm{then}\:\mathrm{det}\left({A}^{−\mathrm{1}} \right) \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by udaythool last updated on 10/Aug/20 $${AA}^{−\mathrm{1}} ={I} \\…
Question Number 41578 by Dawajan Nikmal last updated on 09/Aug/18 $$\mathrm{If}\:\:{u}_{\mathrm{10}} =\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}^{\mathrm{10}} \:\mathrm{sin}\:{x}\:{dx},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${u}_{\mathrm{10}} +\mathrm{90}\:{u}_{\mathrm{8}} \:\:\mathrm{is} \\ $$ Terms of Service Privacy…
Question Number 41579 by Dawajan Nikmal last updated on 09/Aug/18 $$\mathrm{If}\:\:{u}_{\mathrm{10}} =\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}^{\mathrm{10}} \:\mathrm{sin}\:{x}\:{dx},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${u}_{\mathrm{10}} +\mathrm{90}\:{u}_{\mathrm{8}} \:\:\mathrm{is} \\ $$ Commented by maxmathsup by…