Question 1203823

Find all exact solutions on [{{{0}}}, {{{2pi}}}). (Enter your answers as a comma-separated list.)

{{{2cos^2(t) - cos(t) = 1}}}....first factor

{{{cos(t)(2cos(t) - 1 )= 1}}}


solve by substitution


{{{cos(t)=1 }}}in interval [{{{0}}}, {{{2pi}}}) => {{{t=0}}}

{{{cos(t)=-1/2}}} in interval [{{{0}}},{{{ 2pi}}}) => {{{t=2pi/3}}},{{{ t=4pi/3}}}


combine solutions

{{{t=0}}}, {{{t=2pi/3}}}, {{{t= 4pi/3}}}