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 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 $$\mathrm{8}…
Question Number 95515 by bagjamath last updated on 25/May/20 $$\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 $${then}\:{I}\left({m},{n}\right)\:{is}\:{a}\:{Beta}\:{function}…
Question Number 29326 by abdus salam last updated on 07/Feb/18 $$\mathrm{The}\:\mathrm{unit}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{number}\:\mathrm{are}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{unit}\:\mathrm{digit}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{number}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{values}\:\mathrm{are}\: \\ $$$$\mathrm{possible}\:\mathrm{for}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{such} \\ $$$$\mathrm{numbers}? \\ $$ Answered by…
Question Number 94635 by Vishal Sharma last updated on 20/May/20 $$\mathrm{A}\:\mathrm{father}\:\mathrm{with}\:\mathrm{8}\:\mathrm{children}\:\mathrm{takes}\:\mathrm{them} \\ $$$$\mathrm{3}\:\mathrm{at}\:\mathrm{a}\:\mathrm{time}\:\mathrm{to}\:\mathrm{the}\:\mathrm{Gardens},\:\mathrm{as}\:\mathrm{often}\:\mathrm{as} \\ $$$$\mathrm{he}\:\mathrm{can}\:\mathrm{without}\:\mathrm{taking}\:\mathrm{the}\:\mathrm{same}\:\mathrm{3}\:\mathrm{children} \\ $$$$\mathrm{together}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}.\:\mathrm{The}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{times}\:\mathrm{each}\:\mathrm{child}\:\mathrm{will}\:\mathrm{go}\:\mathrm{to}\:\mathrm{the}\:\mathrm{garden} \\ $$$$\mathrm{is} \\ $$ Answered by…
Question Number 94632 by Vishal Sharma last updated on 20/May/20 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{m}} \:\mathrm{and}\:{x}^{{n}} \left({m},\:{n}\:\in\:{N}\right)\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{{m}+{n}} \:\mathrm{are} \\ $$ Commented by mr W last updated on…
Question Number 94628 by Vishal Sharma last updated on 20/May/20 $$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\bigtriangleup\:{ABC}\:\mathrm{is}\:\mathrm{6}\:\mathrm{times} \\ $$$$\mathrm{the}\:\mathrm{arithmetic}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sines}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{angles}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{side}\:{a}\:\mathrm{is}\:\:\mathrm{1},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{angle}\:{A}\:\:\mathrm{is} \\ $$ Answered by Kunal12588 last updated on…
Question Number 94629 by Vishal Sharma last updated on 20/May/20 $$\mathrm{In}\:\bigtriangleup{ABC},\:{a}=\sqrt{\mathrm{3}}+\mathrm{1},\:{B}=\mathrm{30}°,\:{C}=\mathrm{45}°, \\ $$$$\mathrm{then}\:{c}\:=\:\_\_\_\_. \\ $$ Answered by i jagooll last updated on 20/May/20 $$\frac{\mathrm{c}}{\mathrm{sin}\:\mathrm{45}^{\mathrm{o}} }\:=\:\frac{\mathrm{a}}{\mathrm{sin}\:\mathrm{105}^{\mathrm{o}}…