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} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 81532 by Power last updated on 13/Feb/20 Commented by mr W last updated on 13/Feb/20 $${all}\:{options}\:{are}\:{wrong}! \\ $$ Commented by mr W last…
Question Number 15975 by myintkhaing last updated on 16/Jun/17 $${Solve}\:{sin}\:\mathrm{2}{x}\:+\:{cos}\:\mathrm{2}{x}\:=\mathrm{0}, \\ $$$${for}\:−\pi<{x}<\pi. \\ $$ Commented by tawa tawa last updated on 16/Jun/17 $$\mathrm{sin2x}\:+\:\mathrm{cos2x}\:=\:\mathrm{0} \\ $$$$\mathrm{Note}:\:\mathrm{sin2x}\:=\:\mathrm{2sinxcosx}\:\:\mathrm{and}\:\:\mathrm{cos2x}\:=\:\mathrm{cos}^{\mathrm{2}}…
Question Number 147031 by mnjuly1970 last updated on 17/Jul/21 Answered by mindispower last updated on 17/Jul/21 $$\left(\mathrm{1}\right)+\left(\mathrm{2}\right)\Rightarrow{cos}\left({x}\right)+{sin}\left({x}\right)−\sqrt{\mathrm{2}}=\frac{{cos}\left(\mathrm{2}{y}\right)}{\:\sqrt{\mathrm{2}}} \\ $$$$\Rightarrow\sqrt{\mathrm{2}}{cos}\left(\frac{\pi}{\mathrm{4}}−{x}\right)−\sqrt{\mathrm{2}}=\frac{{cos}\left(\mathrm{2}{y}\right)}{\:\sqrt{\mathrm{2}}} \\ $$$$\Rightarrow{cos}\left(\mathrm{2}{y}\right)=\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{4}}−{x}\right)−\mathrm{2} \\ $$$$ \\ $$…
Question Number 147008 by gsk2684 last updated on 17/Jul/21 $${find}\:{the}\:{number}\:{of}\:{values}\:{of}\:\mathrm{cot}\:\theta\: \\ $$$${where}\:\theta\in\left[\frac{\pi}{\mathrm{12}}\:\frac{\pi}{\mathrm{2}}\right]\:{satisfying}\:{the}\: \\ $$$${equation}\:\left[\mathrm{tan}\:\theta.\left[\mathrm{cot}\:\theta\right]\right]=\mathrm{1}\:?\: \\ $$$$\left({where}\:\left[{x}\right]\:{is}\:{greatest}\:{integer}\right. \\ $$$$\left.{less}\:{than}\:{or}\:{equal}\:{to}\:{x}\right) \\ $$ Commented by gsk2684 last updated…