Question 1170579
{{{2sqrt(2)*sin(2t) - sqrt(6)*tan(2t) = 0}}}

let {{{2t = x}}}

{{{2sqrt(2)*sin(x) - sqrt(6)*tan(x) = 0}}}..............{{{tan(x)=sin (x)/cos(x)}}}

{{{2sqrt(2)*sin(x) - sqrt(6)(sin (x)/cos(x)) = 0}}}............times cos(x)

{{{2sqrt(2)*sin(x)cos(x) - sqrt(6)*sin(x) = 0}}}

{{{(2sqrt(2)*cos(x) - sqrt(6))*sin (x) = 0}}}


=> {{{sin (x) = 0}}} =>{{{sin (2t) = 0}}}
{{{t}}} in the interval [{{{0}}}, {{{2pi}}}] : {{{t=0}}}, {{{t= pi/2}}}, {{{t= pi}}} , {{{t= 3pi/2}}}, {{{t=2pi}}}

or
{{{2sqrt(2)*cos(x) - sqrt(6)= 0}}}=>{{{cos(x) = sqrt(6)/2sqrt(2)}}}

=>{{{cos(2t) = sqrt(6)/2sqrt(2)}}}

=>{{{cos(2t) = sqrt(3)/2}}}

{{{2t=cos^-1( sqrt(3)/2)}}}

{{{2t=pi/6 }}} 

{{{t=pi/12 }}}


 {{{t}}} in the interval [{{{0}}},{{{ 2pi}}}] : {{{t=pi/12}}},{{{t=11pi/12}}},{{{t=13pi/12}}},{{{t=23pi/12}}}


combine solutions:

{{{t=0}}}, {{{t= pi/2}}}, {{{t= pi}}} , {{{t= 3pi/2}}}, {{{t=2pi}}},{{{t=pi/12}}},{{{t=11pi/12}}},{{{t=13pi/12}}},{{{t=23pi/12}}}