Question Number 95982 by mpym last updated on 29/May/20 $$\Sigma{x}\left({y}^{\mathrm{3}} −{z}^{\mathrm{3}} \right)=\_\_\_\_\_. \\ $$ Answered by mr W last updated on 29/May/20 $$={x}\left({y}^{\mathrm{3}} −{z}^{\mathrm{3}} \right)+{y}\left({z}^{\mathrm{3}}…
Question Number 30356 by soksan last updated on 21/Feb/18 $$\mathrm{If}\:\mathrm{sin}\:\mathrm{2}\theta=\:\mathrm{cos}\:\mathrm{3}\theta\:\:\mathrm{and}\:\theta\:\mathrm{is}\:\mathrm{an}\:\mathrm{acute} \\ $$$$\mathrm{angle},\:\mathrm{then}\:\mathrm{sin}\:\theta\:\mathrm{equals} \\ $$ Answered by mrW2 last updated on 21/Feb/18 $$\mathrm{sin}\:\mathrm{2}\theta=\:\mathrm{cos}\:\mathrm{3}\theta \\ $$$$\mathrm{2sin}\:\theta\mathrm{cos}\:\theta=\mathrm{4cos}^{\mathrm{3}} \:\theta−\mathrm{3cos}\:\theta…
Question Number 30354 by soksan last updated on 21/Feb/18 $$\mathrm{If}\:\:{g}\left({x}\right)=\overset{{x}} {\int}_{\mathrm{0}} \mathrm{cos}^{\mathrm{4}} {t}\:{dt},\:\mathrm{then}\:{g}\:\left({x}+\pi\right)\:= \\ $$ Answered by ajfour last updated on 21/Feb/18 $${g}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\:\:{x}} \left(\mathrm{2cos}\:^{\mathrm{2}}…
Question Number 30183 by Surajitzzz last updated on 17/Feb/18 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{ax}^{\mathrm{2}} −{bx}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{4}:\:\mathrm{5},\:\mathrm{then}\:\mathrm{4}{b}^{\mathrm{2}} =\mathrm{81}{ac}. \\ $$ Answered by Rasheed.Sindhi last updated on 18/Feb/18 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{are}\:\mathrm{4k}\:\&\:\mathrm{5k} \\…
Question Number 30156 by naybr last updated on 17/Feb/18 $$\mathrm{If}\:\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:{x}+\mathrm{3},\:{y}+\mathrm{3},\:{z}+\mathrm{3}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{HP},\:\mathrm{then} \\ $$ Answered by ajfour last updated on 17/Feb/18 $${Then} \\ $$$$\:\:\:\frac{{y}}{{x}}=\frac{{z}}{{y}}\:={r}\:\:\:{and}\:\:\:\frac{\mathrm{2}}{{y}+\mathrm{3}}=\frac{\mathrm{1}}{{x}+\mathrm{3}}+\frac{\mathrm{1}}{{z}+\mathrm{3}} \\…
Question Number 95597 by bagjamath last updated on 26/May/20 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cosec}^{\mathrm{2}} \:\frac{\pi}{\mathrm{7}}+\mathrm{cosec}^{\mathrm{2}} \:\frac{\mathrm{2}\pi}{\mathrm{7}}+\mathrm{cosec}^{\mathrm{2}} \:\frac{\mathrm{3}\pi}{\mathrm{7}}\:\mathrm{is} \\ $$ Commented by MJS last updated on 26/May/20 $$\mathrm{8}…
Question Number 95598 by bagjamath last updated on 26/May/20 $$\mathrm{If}\:\:\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}} +…+\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:\:\underset{\underset{{i}\:\neq\:{j}} {{i},\:{j}=\mathrm{1}}} {\overset{\mathrm{2}{n}} {\sum}}\:\:\:{x}_{{i}} \:{x}_{{j}} \:= \\ $$…
Question Number 95515 by bagjamath last updated on 25/May/20 $$\mathrm{If}\:{A}+{B}+{C}\:=\:\pi,\:\mathrm{then} \\ $$$$\mathrm{sin}^{\mathrm{2}} {A}+\mathrm{sin}^{\mathrm{2}} {B}+\mathrm{sin}^{\mathrm{2}} {C}−\mathrm{2}\:\mathrm{cos}\:{A}\:\mathrm{cos}\:{B}\:\mathrm{cos}\:{C}= \\ $$ Answered by som(math1967) last updated on 25/May/20 $$\mathrm{sin}^{\mathrm{2}}…
Question Number 95512 by bagjamath last updated on 25/May/20 $$\mathrm{If}\:\:\mathrm{in}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{8}{R}^{\mathrm{2}} =\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} ,\:\mathrm{then} \\ $$$$\mathrm{the}\:\bigtriangleup{ABC}\:\mathrm{is} \\ $$ Commented by som(math1967) last updated on 25/May/20…
Question Number 95378 by Fikret last updated on 24/May/20 $$\mathrm{If}\:\:{I}\:\left({m},\:{n}\right)=\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{{m}−\mathrm{1}} \left(\mathrm{1}−{x}\right)^{{n}−\mathrm{1}} {dx},\:\mathrm{then} \\ $$ Commented by Tony Lin last updated on 24/May/20 $${then}\:{I}\left({m},{n}\right)\:{is}\:{a}\:{Beta}\:{function}…