Question Number 229 by ssahoo last updated on 25/Jan/15 $$\mathrm{If}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral} \\ $$$$\mathrm{traingle}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{circle}\:\mid{z}\mid=\mathrm{2}\:\mathrm{and}\:\mathrm{if} \\ $$$${z}_{\mathrm{1}} =\mathrm{1}+{i}\sqrt{\mathrm{3}},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{z}_{\mathrm{2}} \:\mathrm{and}\:{z}_{\mathrm{3}} . \\ $$ Answered by 123456…
Question Number 131302 by EDWIN88 last updated on 03/Feb/21 $${Given}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{6}}+\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\right)=\:\frac{\mathrm{13}}{\mathrm{14}} \\ $$$$\:{If}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{a}\sqrt{\mathrm{3}}}{{b}}\right)\:{then}\: \\ $$$$\:\frac{{a}+{b}}{\mathrm{2}}\:=?\: \\ $$ Answered by mr W last updated…
Question Number 131296 by EDWIN88 last updated on 03/Feb/21 $$\:{If}\:{a}\mathrm{sin}^{−\mathrm{1}} \left({x}\right)−{b}\mathrm{cos}^{−\mathrm{1}} \left({x}\right)=\:{c}\: \\ $$$${then}\:{the}\:{value}\:{of}\:{a}\mathrm{sin}^{−\mathrm{1}} \left({x}\right)+{b}\mathrm{cos}^{−\mathrm{1}} \left({x}\right)\: \\ $$$$\left({whenever}\:{exists}\right)\:{is}\:{equal}\:{to}\:? \\ $$ Answered by liberty last updated…
Question Number 65760 by mmkkmm000m last updated on 03/Aug/19 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{1}}{\mathrm{9}\:\mathrm{cos}\:{x}+\mathrm{12}\:\mathrm{sin}\:{x}}\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 04/Aug/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
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Question Number 225 by 123456 last updated on 25/Jan/15 $$\boldsymbol{\mathrm{u}}=\mathrm{2}\boldsymbol{\mathrm{i}}+\mathrm{3}\boldsymbol{\mathrm{j}}+\mathrm{5}\boldsymbol{\mathrm{k}} \\ $$$$\boldsymbol{\mathrm{v}}=\mathrm{3}\boldsymbol{\mathrm{i}}+\mathrm{2}\boldsymbol{\mathrm{j}}−\mathrm{5}\boldsymbol{\mathrm{k}} \\ $$$$\boldsymbol{\mathrm{w}}=−\mathrm{2}\boldsymbol{\mathrm{i}}+\mathrm{3}\boldsymbol{\mathrm{j}}+\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{find} \\ $$$$\boldsymbol{\mathrm{u}}\centerdot\left(\boldsymbol{\mathrm{v}}×\boldsymbol{\mathrm{w}}\right)+\left(\boldsymbol{\mathrm{u}}×\boldsymbol{\mathrm{v}}\right)\centerdot\left(\boldsymbol{\mathrm{u}}×\boldsymbol{\mathrm{w}}\right) \\ $$ Answered by mreddy last updated…
Question Number 131298 by liberty last updated on 03/Feb/21 $$\mathrm{Let}\:\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)+\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{2x}\right)+\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{3x}\right)=\pi \\ $$$$.\mathrm{If}\:\mathrm{x}\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{cubic}\:\mathrm{ax}^{\mathrm{3}} +\mathrm{bx}^{\mathrm{2}} +\mathrm{cx}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{a}+\mathrm{b}+\mathrm{c}\:\mathrm{has}\:\mathrm{the}\:\mathrm{value}\:\mathrm{equal}\:\mathrm{to}\: \\ $$ Answered by mr W…
Question Number 224 by 123456 last updated on 25/Jan/15 $$\mathrm{solve} \\ $$$${x}\frac{{dy}}{{dx}}+{y}=\alpha{x}+\beta \\ $$ Answered by mreddy last updated on 16/Dec/14 $$\frac{{dy}}{{dx}}+\frac{{y}}{{x}}=\frac{\alpha{x}+\beta}{{x}} \\ $$$$\mathrm{Integrating}\:\mathrm{Factor}={e}^{\int\frac{\mathrm{1}}{{x}}{dx}} ={e}^{\mathrm{ln}\:{x}}…
Question Number 223 by 123456 last updated on 25/Jan/15 $$\mathrm{ln}\:\left({e}^{\mathrm{2}} \right)+\mathrm{log}_{\mathrm{10}} \left(\mathrm{100}\right) \\ $$ Answered by ghosea last updated on 16/Dec/14 $$\mathrm{ln}\:{e}^{\mathrm{2}} +\mathrm{log}_{\mathrm{10}} \mathrm{10}^{\mathrm{2}} =\mathrm{2}+\mathrm{2}=\mathrm{4}…
Question Number 222 by 123456 last updated on 25/Jan/15 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{\mathrm{arcsin}\:{x}} \\ $$ Answered by ghosea last updated on 16/Dec/14 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{\mathrm{arcsin}\:{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\centerdot\frac{{x}}{\mathrm{arcsin}\:{x}}…