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…
Question Number 19262 by djatmiko last updated on 08/Aug/17 $$\mathrm{Let}\:\boldsymbol{\mathrm{p}},\:\boldsymbol{\mathrm{q}},\:\boldsymbol{\mathrm{r}}\:\mathrm{be}\:\mathrm{three}\:\mathrm{mutually}\:\mathrm{perpendicular} \\ $$$$\mathrm{vectors}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{magnitude}.\:\mathrm{If}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\boldsymbol{\mathrm{x}}\:\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\left.\boldsymbol{\mathrm{p}}\left.\:×\left\{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{q}}\right)×\boldsymbol{\mathrm{p}}\right\}+\boldsymbol{\mathrm{q}}×\left\{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{r}}\right)×\boldsymbol{\mathrm{q}}\right\} \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\:\boldsymbol{\mathrm{r}}×\left\{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{p}}\right)×\boldsymbol{\mathrm{r}}\right\}=\mathrm{0},\:\mathrm{then}\:\boldsymbol{\mathrm{x}}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by} \\ $$ Answered by ajfour…
Question Number 19148 by khamizan833@yahoo.com last updated on 06/Aug/17 $$\mathrm{If} \\ $$$${f}\left({x}\right)=\begin{vmatrix}{\mathrm{sin}\:{x}+\mathrm{sin2}{x}+\mathrm{sin}\:\mathrm{3}{x}}&{\mathrm{sin}\:\mathrm{2}{x}}&{\mathrm{sin}\:\mathrm{3}{x}}\\{\:\:\:\:\:\:\:\:\mathrm{3}+\mathrm{4}\:\mathrm{sin}\:{x}}&{\:\:\:\:\mathrm{3}}&{\mathrm{4}\:\mathrm{sin}\:{x}}\\{\:\:\:\:\:\:\:\:\:\:\mathrm{1}+\mathrm{sin}\:{x}}&{\:\mathrm{sin}\:{x}}&{\:\:\:\:\mathrm{1}}\end{vmatrix} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\left({x}\right)\:{dx}\:\:\:\mathrm{is} \\ $$ Answered by ajfour last updated on 06/Aug/17…
Question Number 19134 by chernoaguero@gmail.com last updated on 05/Aug/17 $$\mathrm{If}\:\frac{\mathrm{1}}{\left(\mathrm{243}\right)^{{x}} }\:=\:\left(\mathrm{729}\right)^{{y}} =\:\mathrm{3}^{\mathrm{3}} ,\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{5}{x}\:+\:\mathrm{6}{y}. \\ $$ Answered by Tinkutara last updated on 05/Aug/17 $$\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{5}{x}}…
Question Number 18969 by chernoaguero@gmail.com last updated on 02/Aug/17 $$\mathrm{If}\:\left(\frac{{a}}{{b}}\right)+\left(\frac{{b}}{{a}}\right)=\mathrm{2},\:\mathrm{then}\:\mathrm{find}\:\left(\frac{{a}}{{b}}\right)^{\mathrm{10}} −\:\left(\frac{{b}}{{a}}\right)^{\mathrm{10}} . \\ $$ Answered by Joel577 last updated on 02/Aug/17 $$\:\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:=\:\mathrm{2}{ab} \\…