Question Number 20434 by pp75718276@gmail.com last updated on 26/Aug/17 $$\mathrm{If}\:\:\mathrm{cos}\:{x}=\mathrm{tan}\:{y},\:\mathrm{cos}\:{y}=\mathrm{tan}\:{z},\:\mathrm{cos}\:{z}=\mathrm{tan}\:{x}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{sin}\:{x}\:\:\mathrm{is} \\ $$ Answered by ajfour last updated on 27/Aug/17 $$\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} {z}=\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}} {z}} \\…
Question Number 20326 by kkr1729 last updated on 25/Aug/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{inegral} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\:\:{abc}\:=\:\mathrm{30}\:\mathrm{is} \\ $$ Commented by Tinkutara last updated on 25/Aug/17 $$\mathrm{30}\:=\:\mathrm{2}\:×\:\mathrm{3}\:×\:\mathrm{5}\:=\:\mathrm{8}\:\mathrm{factors} \\ $$$$\mathrm{Required}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:=\:^{\mathrm{8}} {C}_{\mathrm{3}}…
Question Number 85846 by Jakir Sarif Mondal last updated on 25/Mar/20 $$\underset{\:\mathrm{0}} {\overset{\mathrm{50}\pi} {\int}}\:\mid\:\mathrm{cos}\:{x}\:\mid{dx}\:= \\ $$ Commented by jagoll last updated on 25/Mar/20 $$\mathrm{100}×\int\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}}…
Question Number 85739 by Jakir Sarif Mondal last updated on 24/Mar/20 $$\mathrm{If}\:{F}\:\left({x}\right)=\underset{{x}^{\mathrm{2}} } {\overset{{x}^{\mathrm{3}} } {\int}}\:\mathrm{log}\:{t}\:{dt}\:\:\left({x}>\mathrm{0}\right),\:\mathrm{then}\:{F}\:'\left({x}\right)= \\ $$ Answered by john santu last updated on…
Question Number 19809 by CheaV last updated on 16/Aug/17 $$\mathrm{If}\:\mathrm{sin}\:\theta+\mathrm{cosec}\:\theta=\mathrm{2},\:\mathrm{then}\:\mathrm{sin}^{\mathrm{2}} \theta+\mathrm{cosec}^{\mathrm{2}} \theta \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by ajfour last updated on 16/Aug/17 $$\left(\mathrm{sin}\:\theta+\mathrm{cosec}\:\theta\right)^{\mathrm{2}} =\mathrm{sin}\:^{\mathrm{2}}…
Question Number 85315 by sinus last updated on 20/Mar/20 $$\mathrm{The}\:\mathrm{largest}\:\mathrm{interval}\:\mathrm{in}\:\mathrm{which}\:{x}\:\mathrm{lies} \\ $$$$\mathrm{satisfying}\:{x}^{\mathrm{12}} −{x}^{\mathrm{9}} +{x}^{\mathrm{4}} −{x}+\mathrm{1}>\mathrm{0}\:\mathrm{is} \\ $$ Commented by mr W last updated on 20/Mar/20…
Question Number 85280 by Jakir Sarif Mondal last updated on 20/Mar/20 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)\:{dx}\:= \\ $$ Answered by mind is power last updated…
Question Number 19382 by chernoaguero@gmail.com last updated on 10/Aug/17 $$\mathrm{If}\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{9}^{{x}−\mathrm{1}} +\mathrm{7}\right)−\mathrm{log}_{\mathrm{2}} \left(\mathrm{3}^{{x}−\mathrm{1}} +\mathrm{1}\right)=\mathrm{2},\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{are} \\ $$ Answered by khamizan833@yahoo.com last updated on 10/Aug/17…
Question Number 84862 by Jakir Sarif Mondal last updated on 25/Mar/20 $$\underset{\:\mathrm{0}} {\overset{\mathrm{100}} {\int}}\:\left[\mathrm{tan}^{−\mathrm{1}} {x}\right]{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\boldsymbol{{Jakir}}\:\boldsymbol{{Sarif}}\:\:\boldsymbol{{Mondal}}. \\ $$$$\:\:\:\:\:\:\: \\ $$ Commented by mr W…
Question Number 84861 by Jakir Sarif Mondal last updated on 16/Mar/20 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{function},\:\mathrm{then} \\ $$$$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx}\:=\:\mathrm{2}\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx} \\ $$ Commented by mr W last…