Question Number 22714 by selestian last updated on 22/Oct/17 Answered by ajfour last updated on 22/Oct/17 $$\lambda\:={a}+{b}+{c}\: \\ $$$${let}\:\:\:{l}={b}\mathrm{cos}\:^{\mathrm{2}} \left(\frac{{C}}{\mathrm{2}}\right)+{c}\mathrm{cos}\:^{\mathrm{2}} \left(\frac{{B}}{\mathrm{2}}\right) \\ $$$$\Rightarrow\:\:\:\:\mathrm{2}{l}={b}\left(\mathrm{1}+\mathrm{cos}\:{C}\right)+{c}\left(\mathrm{1}+\mathrm{cos}\:{B}\right) \\ $$$$\Rightarrow\:\:\:\:\mathrm{2}{l}={b}+{c}+\left({b}\mathrm{cos}\:{C}+{c}\mathrm{cos}\:{B}\right)…
Question Number 153758 by yeti123 last updated on 10/Sep/21 $${S}\:=\:\frac{\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}\left(\theta_{{k}} \right)}{\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{cos}\left(\theta_{{k}} \right)};\:\mathrm{where}\:\left(\theta_{{k}} \right)_{{k}\:=\:\mathrm{1}} ^{{n}} \:\mathrm{is}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression}. \\ $$$$\mathrm{show}\:\mathrm{that}\:{S}\:=\:\mathrm{tan}\left(\bar {\theta}\right) \\ $$$$\mathrm{where}\:\bar {\theta}\:=\:\frac{\mathrm{1}}{{n}}\underset{{k}\:=\:\mathrm{1}}…
Question Number 88218 by mathocean1 last updated on 09/Apr/20 Commented by mathocean1 last updated on 09/Apr/20 $$\mathrm{This}\:\mathrm{is}\:\mathrm{face}\:\mathrm{view}\:\mathrm{of}\:\mathrm{an}\:\mathrm{evacuation}\: \\ $$$$\mathrm{canal}.\:\mathrm{It}\:\mathrm{has}\:\mathrm{a}\:\mathrm{trapeze}\:\mathrm{form}.\:\mathrm{4m} \\ $$$$\mathrm{represents}\:\mathrm{its}\:\mathrm{small}\:\mathrm{base}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determinate}\:\:\theta\:\in\:\left[\mathrm{60};\mathrm{90}\right]\:\mathrm{such}\:\mathrm{as}\:\mathrm{the}\: \\ $$$$\mathrm{capacity}\:\mathrm{of}\:\mathrm{canal}\:\mathrm{is}\:\mathrm{maximal}.…
Question Number 153742 by Babatunde last updated on 09/Sep/21 Answered by liberty last updated on 10/Sep/21 $${t}={e}^{\mathrm{ln}\:\mathrm{2}^{\left(\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{6}} {x}+…\right)} } \:=\:\mathrm{2}^{\frac{\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}}} \\…
Question Number 22649 by ajfour last updated on 21/Oct/17 Commented by ajfour last updated on 21/Oct/17 $${solution}\:{to}\:{Q}.\mathrm{22599} \\ $$ Answered by ajfour last updated on…
Question Number 153708 by liberty last updated on 09/Sep/21 Answered by MJS_new last updated on 09/Sep/21 $$\left(\mathrm{1}\right)\:\mathrm{200}{x}+\mathrm{160}{y}=\mathrm{300} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{200}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }=\mathrm{160}\sqrt{\mathrm{1}−{y}^{\mathrm{2}} } \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:{y}=\frac{\mathrm{15}−\mathrm{10}{x}}{\mathrm{8}}…
Question Number 22576 by ajfour last updated on 20/Oct/17 Commented by ajfour last updated on 20/Oct/17 $${Q}.\:\mathrm{22536}\:\left({Alternate}\:{solution}\right) \\ $$ Answered by ajfour last updated on…
Question Number 22536 by NECx last updated on 20/Oct/17 $${show}\:{that}\:\frac{\left({a}+{b}+{c}\right)^{\mathrm{2}} }{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }= \\ $$$$\frac{\mathrm{cot}\:\frac{\mathrm{1}}{\mathrm{2}}{A}+\mathrm{cot}\:\frac{\mathrm{1}}{\mathrm{2}}{B}+\mathrm{cot}\:\frac{\mathrm{1}}{\mathrm{2}}{C}}{\mathrm{cot}\:{A}+\mathrm{cot}\:{B}+\mathrm{cot}\:{C}} \\ $$$$ \\ $$$$ \\ $$$${please}\:{help} \\ $$ Commented…
Question Number 153568 by liberty last updated on 08/Sep/21 $${solve}\:{in}\:{x}\in\mathbb{C} \\ $$$$\:\mathrm{sin}\:{x}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$ \\ $$ Answered by Ar Brandon last updated on 08/Sep/21 $$\mathrm{sin}{x}=\frac{\mathrm{3}}{\mathrm{2}}\:\Rightarrow{e}^{{ix}}…
Question Number 153532 by talminator2856791 last updated on 08/Sep/21 $$\: \\ $$$$\:\mathrm{sin}\left(\mathrm{sin}\left(\mathrm{sin}\left({x}^{\mathrm{2}\pi{x}} −\mathrm{1}\right)\right)\right)\:=\:\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}^{\mathrm{2}{ex}} +\mathrm{1}\right)\right)\right)\: \\ $$$$\:{x}\:=\:? \\ $$$$\: \\ $$ Terms of Service Privacy Policy…