Question Number 16179 by Tinkutara last updated on 24/Jun/17 $$\mathrm{If}\:{a}\:>\:\mathrm{0},\:{b}\:>\:\mathrm{0}\:\mathrm{and}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:{a}\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:{b}\:\mathrm{cosec}^{\mathrm{2}} \:\theta\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{a}\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:{b}\:\mathrm{cos}^{\mathrm{2}} \:\theta, \\ $$$$\mathrm{then}\:\frac{{a}}{{b}}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\left[\boldsymbol{\mathrm{Answer}}:\:\mathrm{4}\right] \\ $$ Answered by ajfour…
Question Number 16093 by Tinkutara last updated on 17/Jun/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mid\mathrm{sin}\:{x}\mid\:=\:\mathrm{tan}\:{x}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{4}\pi\right]\:\mathrm{is}/\mathrm{are}? \\ $$ Commented by Tinkutara last updated on 17/Jun/17 $$\mathrm{My}\:\mathrm{answer}\:\mathrm{comes}\:\mathrm{out}\:\mathrm{to}\:\mathrm{be}\:\mathrm{5}\:\mathrm{but} \\ $$$$\mathrm{answer}\:\mathrm{in}\:\mathrm{book}\:\mathrm{is}\:\mathrm{6}.\:\mathrm{How}? \\…
Question Number 16090 by Tinkutara last updated on 17/Jun/17 $$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mid\sqrt{\mathrm{sin}^{\mathrm{2}} \:{x}\:+\:\mathrm{2}{a}^{\mathrm{2}} }\:−\:\sqrt{\mathrm{2}{a}^{\mathrm{2}} \:−\:\mathrm{3}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}}\mid; \\ $$$$\mathrm{where}\:'{a}'\:\mathrm{and}\:'{x}'\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers},\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\sqrt{\mathrm{2}} \\…
Question Number 16092 by Tinkutara last updated on 17/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\in\:\left[\mathrm{0},\:\mathrm{2}\pi\right] \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{sin}\:{x}\:>\:\mathrm{cos}\:{x}. \\ $$$$\left(\mathrm{1}\right)\:\left(\frac{\pi}{\mathrm{4}},\:\frac{\mathrm{3}\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$$$\left(\mathrm{3}\right)\:\left(\frac{\pi}{\mathrm{4}},\:\frac{\mathrm{5}\pi}{\mathrm{4}}\right) \\ $$$$\left(\mathrm{4}\right)\:\left(\mathrm{0},\:\frac{\mathrm{3}\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$ Commented by Tinkutara…
Question Number 16089 by Tinkutara last updated on 17/Jun/17 $$\mathrm{The}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function} \\ $$$${f}\left(\theta\right)\:=\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \:\theta}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left[\mathrm{1},\:\infty\right) \\ $$$$\left(\mathrm{2}\right)\:\left[\mathrm{2},\:\infty\right) \\ $$$$\left(\mathrm{3}\right)\:\left[\mathrm{1},\:\frac{\mathrm{3}}{\mathrm{2}}\right] \\ $$$$\left(\mathrm{4}\right)\:\left[\frac{\mathrm{3}}{\mathrm{2}},\:\infty\right) \\ $$ Commented…
Question Number 147157 by olohuntosin last updated on 18/Jul/21 $${proof}\:{that}\:{tan}\emptyset+\mathrm{sesin}\:\mathrm{c}\emptyset/{tan}\emptyset+{sec}\emptyset\:=\:\mathrm{1}+{sin}\emptyset/{cos}\emptyset \\ $$ Commented by puissant last updated on 18/Jul/21 $$\mathrm{i}\:\mathrm{do}\:\mathrm{no}\:\mathrm{see}.. \\ $$ Terms of Service…
Question Number 147118 by bramlexs22 last updated on 18/Jul/21 Answered by Olaf_Thorendsen last updated on 20/Jul/21 $$\mathrm{As}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{is}\:\mathrm{45}°\:\mathrm{the}\:\mathrm{cylinder}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{developped}\:\mathrm{as}\:\mathrm{a}\:\mathrm{square}. \\ $$$$\mathrm{The}\:\mathrm{walk}\:\mathrm{is}\:\mathrm{the}\:\mathrm{diagonal}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}. \\ $$$${l}\:=\:\sqrt{\mathrm{2}}{h}\:=\:\mathrm{9}\sqrt{\mathrm{2}} \\ $$…
Question Number 16041 by Tinkutara last updated on 17/Jun/17 $$\mathrm{If}\:\mathrm{sides}\:{a},\:{b},\:{c}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{are}\:\mathrm{in}\:\mathrm{H}.\mathrm{P}., \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{sin}^{\mathrm{2}} \:\left(\frac{{A}}{\mathrm{2}}\right),\:\mathrm{sin}^{\mathrm{2}} \:\left(\frac{{B}}{\mathrm{2}}\right),\:\mathrm{sin}^{\mathrm{2}} \:\left(\frac{{C}}{\mathrm{2}}\right) \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{H}.\mathrm{P}. \\ $$ Answered by Tinkutara last updated on…
Question Number 16039 by Tinkutara last updated on 17/Jun/17 Commented by RasheedSoomro last updated on 17/Jun/17 $$\mathrm{c}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{2ab}\:\mathrm{cos}\:\mathrm{60}° \\ $$$$\mathrm{c}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{ab}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{a}^{\mathrm{2}}…
Question Number 16037 by ajfour last updated on 17/Jun/17 Commented by ajfour last updated on 17/Jun/17 $${In}\:{response}\:{to}\:{Q}.\:\mathrm{16000} \\ $$ Terms of Service Privacy Policy Contact:…