Question Number 209781 by alusto22 last updated on 21/Jul/24 $$\:\:\:\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{40}°−\mathrm{cos}\:\mathrm{40}°}{\mathrm{1}+\mathrm{sin}\:\mathrm{40}°+\mathrm{cos}\:\mathrm{40}°}\:=? \\ $$ Answered by efronzo1 last updated on 21/Jul/24 $$\:\:\:\:\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{40}°−\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{20}°\right)}{\mathrm{1}+\mathrm{sin}\:\mathrm{40}°+\mathrm{2cos}\:^{\mathrm{2}} \mathrm{20}−\mathrm{1}}\: \\ $$$$\:\:=\:\frac{\mathrm{2sin}\:\mathrm{20}°\left(\mathrm{cos}\:\mathrm{20}°+\mathrm{sin}\:\mathrm{20}°\right)}{\mathrm{2cos}\:\mathrm{20}°\left(\mathrm{cos}\:\mathrm{20}°+\mathrm{sin}\:\mathrm{20}°\right)} \\…
Question Number 209783 by Ismoiljon_008 last updated on 21/Jul/24 Answered by mr W last updated on 21/Jul/24 Commented by mr W last updated on 21/Jul/24…
Question Number 209794 by Ismoiljon_008 last updated on 21/Jul/24 $$\:\:\: \\ $$$$\:\:\:\mathrm{13456622577532674}\:{how}\:{many}\:\mathrm{5}-{digit} \\ $$$$\:\:\:{numbers}\:{can}\:{be}\:{made}\:{from}\:{these}\:{numbers}? \\ $$$$\:\:\:{help}\:{please} \\ $$$$ \\ $$ Answered by MM42 last updated…
Question Number 209768 by OmoloyeMichael last updated on 20/Jul/24 $$\boldsymbol{{Express}}\:\boldsymbol{{tan}}\left(\mathrm{3}\right)\:\boldsymbol{{in}}\:\boldsymbol{{surd}}\:\boldsymbol{{form}} \\ $$ Answered by Frix last updated on 22/Jul/24 $$\mathrm{tan}\:\left(\alpha−\beta\right)\:=\frac{\mathrm{tan}\:\alpha\:−\mathrm{tan}\:\beta}{\mathrm{1}+\mathrm{tan}\:\alpha\:\mathrm{tan}\:\beta} \\ $$$$\mathrm{Use}\:\alpha=\mathrm{18}°\:\mathrm{and}\:\beta=\mathrm{15}°.\:\mathrm{The}\:\mathrm{only}\:\mathrm{problem}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{factorize}\:\mathrm{it}… \\…
Question Number 209744 by peter frank last updated on 20/Jul/24 Answered by mr W last updated on 20/Jul/24 $${X}={Y}=\frac{\mathrm{180}−\mathrm{40}}{\mathrm{2}}=\mathrm{70}° \\ $$ Answered by Spillover last…
Question Number 209761 by pablo1234523 last updated on 20/Jul/24 $${x}^{\mathrm{3}} −\mathrm{9}{xy}^{\mathrm{2}} =\mathrm{28} \\ $$$${x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} =\mathrm{15} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y}. \\ $$$${x},{y}\in\mathbb{R} \\ $$ Answered by mr…
Question Number 209746 by MM42 last updated on 21/Jul/24 $$\left.{Q}\right){Choose}\:{at}\:{least}\:{some}\:{members} \\ $$$${frome}\:{the}\:{set}\:{A}=\left\{\mathrm{14},\mathrm{15},…,\mathrm{20},\mathrm{22},\mathrm{23},…,\mathrm{28}\right\} \\ $$$${so}\:{that}\:{whith}\:{confidence}\:\:{includes}\:{three}\:{consecutive} \\ $$$${members}? \\ $$ Commented by MM42 last updated on 20/Jul/24…
Question Number 209763 by Ismoiljon_008 last updated on 20/Jul/24 Commented by Ismoiljon_008 last updated on 20/Jul/24 $$\:\:\:\mathscr{F}{ind}\:{the}\:{number}\:{of}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:{equation}\:{in}\:{the}\:{interval}\:\left[\:−\mathrm{2}\pi;\mathrm{2}\pi\:\right] \\ $$$$\:\:\:{help}\:{please} \\ $$ Answered by…
Question Number 209709 by Ismoiljon_008 last updated on 19/Jul/24 $$ \\ $$$$\:\:\:\int\left({sinx}+{cosx}\right)^{\mathrm{11}} {dx}=\:? \\ $$$$\:\:\:{help}\:{me}\:{please} \\ $$ Answered by mr W last updated on 19/Jul/24…
Question Number 209706 by mr W last updated on 19/Jul/24 $${find}\:{the}\:{sum}\:{of}\: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+…+\mathrm{sin}^{\mathrm{2}} \:\mathrm{60}°=? \\ $$ Answered by BaliramKumar last updated on 19/Jul/24…