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 $$\mathrm{A}\:\mathrm{certain}\:\mathrm{person}'\mathrm{s}\:\mathrm{blood}\:\mathrm{preassure} \\ $$$$\mathrm{is}\:\mathrm{modelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{p}\left(\mathrm{t}\right)=\mathrm{115}+\mathrm{25}\:\mathrm{sin}\:\left(\mathrm{160}\pi\mathrm{t}\right) \\ $$$$\mathrm{where}\:\mathrm{p}\left(\mathrm{t}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{pressure}\:\mathrm{in}\:\mathrm{mmHg} \\ $$$$\mathrm{at}\:\mathrm{time}\:\mathrm{t}\:\mathrm{measured}\:\mathrm{in}\:\mathrm{minutes}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{heartbeats}\:\mathrm{per}\:\mathrm{minute} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{blood}\:\mathrm{preassure} \\ $$$$\mathrm{reading}.\:\mathrm{How}\:\mathrm{does}\:\mathrm{this}\:\mathrm{compare}\: \\…
Question Number 132850 by bramlexs22 last updated on 17/Feb/21 Answered by talminator2856791 last updated on 17/Feb/21 $$\:\mathrm{6}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 1675 by hhhggvghhh last updated on 31/Aug/15 $${scv}\mathrm{2}\left\{{bb}\mathrm{3}{vjhkhbkj}\right\} \\ $$$${nnmvhkvgj}\mathrm{6}{vvfukfjjkhnkgwqqkin} \\ $$$${ckkmnbmbjknn} \\ $$ Answered by 123456 last updated on 31/Aug/15 $${f}_{\omega} \left({z}\right)=\underset{{z}_{\mathrm{0}}…
Question Number 67083 by lalitchand last updated on 22/Aug/19 $$\mathrm{CosA}+\mathrm{CosB}+\mathrm{CosC}=\mathrm{1}+\mathrm{4Cos}\left(\frac{\mathrm{B}+\mathrm{C}}{\mathrm{2}}\right).\mathrm{Cos}\left(\frac{\mathrm{C}+\mathrm{A}}{\mathrm{2}}\right).\mathrm{Cos}\left(\frac{\mathrm{A}+\mathrm{B}}{\mathrm{2}}\right)=\mathrm{1}+\mathrm{4Cos}\left(\frac{\Pi−\mathrm{A}}{\mathrm{4}}\right).\mathrm{Cos}\left(\frac{\Pi−\mathrm{B}}{\mathrm{4}}\right).\mathrm{Cos}\left(\frac{\Pi−\mathrm{C}}{\mathrm{4}}\right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{if}\:\mathrm{A}+\mathrm{B}+\mathrm{C}=\Pi \\ $$ Answered by Tanmay chaudhury last updated on 23/Aug/19 $${LHS} \\ $$$$\mathrm{2}{cos}\left(\frac{{A}+{B}}{\mathrm{2}}\right){cos}\left(\frac{{A}−{B}}{\mathrm{2}}\right)+\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 132531 by bemath last updated on 15/Feb/21 $$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2sin}\:\mathrm{x}+\mathrm{3}}−\sqrt{\mathrm{sin}\:\mathrm{x}+\mathrm{1}} \\ $$ Answered by liberty last updated on 15/Feb/21 $$\frac{\mathrm{df}\left(\mathrm{x}\right)}{\mathrm{dx}}=\frac{\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{2sin}\:\mathrm{x}+\mathrm{3}}}−\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{2}\sqrt{\mathrm{sin}\:\mathrm{x}+\mathrm{1}}}\:=\mathrm{0} \\ $$$$\:\frac{\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{2sin}\:\mathrm{x}+\mathrm{3}}}\:=\:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{2}\sqrt{\mathrm{sin}\:\mathrm{x}+\mathrm{1}}} \\…
Question Number 1407 by 112358 last updated on 29/Jul/15 $${Solve}\:{the}\:{following}\:{inequality} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{sinx}+\mathrm{1}}{{cosx}}\leqslant\mathrm{1} \\ $$$${where}\:\mathrm{0}\leqslant{x}<\mathrm{2}\pi\:,\:{cosx}\neq\mathrm{0} \\ $$ Commented by 123456 last updated on 29/Jul/15 $${f}\left({x}\right)=\frac{\mathrm{sin}\:{x}+\mathrm{1}}{\mathrm{cos}\:{x}} \\…