Question Number 67464 by lalitchand last updated on 27/Aug/19 $$\mathrm{prove}\:\:\:\mathrm{Cos}\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{Cos}\left(\frac{\mathrm{4}\pi}{\mathrm{7}}\right)+\mathrm{Cos}\left(\frac{\mathrm{8}\pi}{\mathrm{7}}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mind is power last updated on 27/Aug/19 $${Z}^{\mathrm{7}} −\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\left({z}−\mathrm{1}\right)\left(\mathrm{1}+{z}+{z}^{\mathrm{2}}…
Question Number 1890 by Rasheed Soomro last updated on 21/Oct/15 $${Solve}\:{for}\:{x} \\ $$$$\:\:\:\:\:\:{tan}\:{x}\:+{tan}\:\mathrm{2}{x}\:−{tan}\:\mathrm{3}{x}\:=\mathrm{0} \\ $$$${Some}\:{one}\:{had}\:{posted}\:{this}\:{question}\:{and}\:{I}\:{had}\:{answered}\:{it} \\ $$$${but}\:{then}\:{thread}\:{was}\:{deleted}! \\ $$$${I}\:{think}\:{that}\:{the}\:{question}\:{is}\:{not}\:{importanceless}\:,\:{so}\:{I}\:{hav} \\ $$$${reposted}\:{it}. \\ $$ Commented by…
Question Number 1870 by alib last updated on 18/Oct/15 $${Solve}\: \\ $$$$ \\ $$$$\mathrm{2}{sin}\:\mathrm{2}{x}−\:\mathrm{3}\left({sin}\:{x}\:+\:{cos}\:{x}\right)\:+\:\mathrm{2}\:=\mathrm{0} \\ $$ Answered by 112358 last updated on 19/Oct/15 $$\mathrm{2}{sin}\mathrm{2}{x}−\mathrm{3}\left({sinx}+{cosx}\right)+\mathrm{2}=\mathrm{0} \\…
Question Number 67396 by Cmr 237 last updated on 26/Aug/19 Commented by mathmax by abdo last updated on 26/Aug/19 $${let}\:{P}\left({z}\right)\:=\:{z}^{\mathrm{2}{n}} \:+\mathrm{1}\:{let}\:{determine}\:{the}\:{roots}\:{of}\:{P}\left({z}\right) \\ $$$${P}\left({z}\right)=\mathrm{0}\:\Leftrightarrow\:{z}^{\mathrm{2}{n}} \:=−\mathrm{1}\:\:\Leftrightarrow\:\:{z}^{\mathrm{2}{n}} ={e}^{{i}\left(\mathrm{2}{k}+\mathrm{1}\right)\pi}…
Question Number 1830 by 112358 last updated on 10/Oct/15 $${Show}\:{that}\:{given} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}{cos}\frac{\pi}{\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{3}}{sin}\frac{\pi}{\mathrm{3}}=\mathrm{5} \\ $$$${then} \\ $$$$\:\:\:\:\:\:\:\pi=\mathrm{3}{cos}^{−\mathrm{1}} \left(\frac{\mathrm{5}}{\:\sqrt{\mathrm{28}}}\right)+\mathrm{3}{tan}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\:. \\ $$ Answered by Rasheed Soomro last…
Question Number 1812 by 112358 last updated on 04/Oct/15 $${Find}\:{the}\:{period}\:{of}\:{f}\left({x}\right)\:{where} \\ $$$${f}\left({x}\right)={cos}\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{3}}\right)+{sin}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}−\frac{\pi}{\mathrm{4}}\right). \\ $$$${How}\:{may}\:{one}\:{find}\:{the}\:{period} \\ $$$${of}\:{the}\:{following}\:{functions} \\ $$$${if}\:\psi\left({x}\right)\:{has}\:{period}\:{m}\:{and}\:\gamma\left({x}\right) \\ $$$${has}\:{period}\:{n}? \\ $$$$\left(\mathrm{1}\right)\:{f}_{\mathrm{1}} \left({x}\right)=\psi\left({x}\right)\gamma\left({x}\right) \\ $$$$\left(\mathrm{2}\right)\:{f}_{\mathrm{2}}…
Question Number 1808 by alib last updated on 04/Oct/15 $$\boldsymbol{\mathcal{P}}{rove}\:\:\mathrm{sin}\:\left({a}\right)+\mathrm{sin}\:\left({a}+\frac{\mathrm{14}\pi}{\mathrm{3}}\right)+\mathrm{sin}\:\left({a}−\frac{\mathrm{8}\pi}{\mathrm{3}}\right)=\mathrm{0}/ \\ $$$$ \\ $$ Answered by 112358 last updated on 05/Oct/15 $${Using}\:{the}\:{compound}\:{angle}\:{formula} \\ $$$${sin}\left({x}\pm{y}\right)={sinxcosy}\pm{cosxsiny}\:{we}\:{get} \\…
Question Number 67345 by Aditya789 last updated on 26/Aug/19 $$\mathrm{3}{sinx}+\mathrm{5}{cosx}=\mathrm{5}\:{then}\:{prove}\:{that}\: \\ $$$$\mathrm{5}{sinx}−\mathrm{3}{cox}=\:+\mathrm{3} \\ $$ Answered by $@ty@m123 last updated on 26/Aug/19 $$\frac{\mathrm{3}}{\mathrm{5}}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\mathrm{1} \\ $$$$\frac{\mathrm{1}−\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}=\frac{\mathrm{3}}{\mathrm{5}} \\…
Question Number 1809 by alib last updated on 04/Oct/15 $$\mathrm{tan}\:{a}+\mathrm{cot}\:{a}+\mathrm{tan}\:\mathrm{3}{a}+\mathrm{cot}\:\mathrm{3}{a}=\frac{\mathrm{8cos}\:^{\mathrm{2}} \mathrm{2}{a}}{\mathrm{sin}\:\mathrm{6}{a}} \\ $$$$ \\ $$ Commented by alib last updated on 04/Oct/15 $$\boldsymbol{{prove}} \\ $$…
Question Number 132866 by bramlexs22 last updated on 17/Feb/21 $$\mathrm{A}\:\mathrm{certain}\:\mathrm{person}'\mathrm{s}\:\mathrm{blood}\:\mathrm{preassure} \\ $$$$\mathrm{is}\:\mathrm{modelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{p}\left(\mathrm{t}\right)=\mathrm{115}+\mathrm{25}\:\mathrm{sin}\:\left(\mathrm{160}\pi\mathrm{t}\right) \\ $$$$\mathrm{where}\:\mathrm{p}\left(\mathrm{t}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{pressure}\:\mathrm{in}\:\mathrm{mmHg} \\ $$$$\mathrm{at}\:\mathrm{time}\:\mathrm{t}\:\mathrm{measured}\:\mathrm{in}\:\mathrm{minutes}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{heartbeats}\:\mathrm{per}\:\mathrm{minute} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{blood}\:\mathrm{preassure} \\ $$$$\mathrm{reading}.\:\mathrm{How}\:\mathrm{does}\:\mathrm{this}\:\mathrm{compare}\: \\…