Question Number 63747 by Tony Lin last updated on 08/Jul/19 $${What}\:{does}\:{sin}^{−\mathrm{2}} {x}\:{mean}? \\ $$ Commented by MJS last updated on 08/Jul/19 $$\mathrm{that}'\mathrm{s}\:\mathrm{the}\:\mathrm{question}… \\ $$$$\mathrm{we}'\mathrm{re}\:\mathrm{not}\:\mathrm{consequent}\:\mathrm{in}\:\mathrm{these}\:\mathrm{things} \\…
Question Number 63703 by kaivan.ahmadi last updated on 07/Jul/19 $${sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}{sin}\mathrm{2}{x}\:\::{x}\in\left[\mathrm{0},\mathrm{2}\pi\right]. \\ $$$${find}\:\:{x} \\ $$ Commented by Prithwish sen last updated on 08/Jul/19 $$\left(\mathrm{sinx}\:+\:\mathrm{cosx}\:\right)\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin2x}\right)\:−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin2x}\right)=\mathrm{0}…
Question Number 129234 by bemath last updated on 14/Jan/21 $$\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{47}°+\mathrm{cos}^{\mathrm{2}} \:\:\mathrm{73}°+\mathrm{cos}\:\mathrm{47}°\mathrm{cos}\:\mathrm{73}°+\frac{\mathrm{1}}{\mathrm{2}}=? \\ $$ Answered by liberty last updated on 14/Jan/21 $$\left(\mathrm{cos}\:\mathrm{73}°+\mathrm{cos}\:\mathrm{47}°\right)^{\mathrm{2}} −\mathrm{cos}\:\mathrm{73}°\mathrm{cos}\:\mathrm{47}°+\frac{\mathrm{1}}{\mathrm{2}}= \\ $$$$\left(\mathrm{2cos}\:\mathrm{60}°\mathrm{cos}\:\mathrm{13}°\right)^{\mathrm{2}}…
Question Number 129233 by MrJoe last updated on 14/Jan/21 $${prove}\:{that} \\ $$$${sin}\:\mathrm{3}{x}=\mathrm{2}{cos}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right){sin}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right) \\ $$ Commented by MrJoe last updated on 15/Jan/21 $${then}\: \\ $$$${if}\:{sin}\left(\mathrm{3}{x}\right)={sin}\left[\mathrm{2}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)\right] \\…
Question Number 129231 by liberty last updated on 14/Jan/21 $$\:\mathrm{Given}\:\begin{cases}{{a}=\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}\\{{b}=\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{2}{x}}\end{cases}.\:\mathrm{If}\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{3}\right)=\mathrm{cos}\:\mathrm{2}{x}+\mathrm{3cos}\:{x} \\ $$$$\mathrm{then}\:{x}\:=? \\ $$ Answered by MJS_new last updated on 14/Jan/21…
Question Number 63693 by Rio Michael last updated on 07/Jul/19 $${find}\:{the}\:{general}\:{solution}\:{for}\: \\ $$$$\:{sin}\mathrm{5}\theta+{sin}\mathrm{3}\theta=\:\mathrm{1} \\ $$ Commented by Prithwish sen last updated on 07/Jul/19 $$\mathrm{sin5}\theta+\mathrm{sin3}\theta=\mathrm{1} \\…
Question Number 63682 by Annmuema last updated on 07/Jul/19 $${given}\:{diameter}\:\mathrm{25}{mm} \\ $$$${half}\:{of}\:{the}\:{drill}\:{point}\:{angle}\:=\mathrm{60} \\ $$$${cutting}\:{velocity}=\mathrm{44000}{mm}/{minute} \\ $$$${length}=\mathrm{60}{mm} \\ $$$${feedrate}=\mathrm{0}.\mathrm{25}{mm}/{revolution} \\ $$$${determine}\:{the}\:{time}\:{needed}\:{to}\:{drill}\:{a}\:{through}\:{hole} \\ $$ Terms of Service…
Question Number 129181 by liberty last updated on 13/Jan/21 $$\:\mathrm{Given}\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{5tan}\:\mathrm{x}=\mathrm{3}\:\mathrm{has}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{are}\:\mathrm{x}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{x}_{\mathrm{2}} .\:\mathrm{Find}\:\mid\:\mathrm{cos}\:\mathrm{x}_{\mathrm{1}} .\mathrm{cos}\:\mathrm{x}_{\mathrm{2}} \:\mid\:. \\ $$ Commented by MJS_new last updated on…
Question Number 63643 by vajpaithegrate@gmail.com last updated on 06/Jul/19 $$\mathrm{P}\left(\alpha,\beta\right)\:\mathrm{Q}\left(\gamma,\delta\right)\:\mathrm{are}\:\mathrm{two}\:\mathrm{points}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{curve} \\ $$$$\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{y}\right)+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{y}\right)+\mathrm{y}^{\mathrm{2}} +\mathrm{2y}=\mathrm{0}\:\mathrm{on} \\ $$$$\mathrm{XY}\:\mathrm{plane}.\mathrm{If}\:\mathrm{d}=\mathrm{PQ}\:\mathrm{then}\:\mathrm{cos}\:\mathrm{d}= \\ $$$$\mathrm{ans}:\pm\mathrm{2n}\pi,\mathrm{n}\in\mathrm{N} \\ $$ Answered by MJS last…
Question Number 129073 by amns last updated on 12/Jan/21 $$\boldsymbol{{Prove}}\:\boldsymbol{{that}}: \\ $$$${sec}^{\mathrm{4}} \theta\:−\:{sec}^{\mathrm{2}} \theta\:=\:{tan}^{\mathrm{4}} \theta\:+\:{tan}^{\mathrm{2}} \theta \\ $$$${Please}\:{help}\:{me}\:{quickly}! \\ $$ Commented by benjo_mathlover last updated…