Question 1151360
{{{2sin^2(x)cos(x)=cos(x)}}}


{{{2sin^2(x)cos(x)-cos(x)=0}}}


{{{(2sin^2(x)-1)cos(x)=0}}}......factor {{{2sin^2(x)-1}}} =>{{{(sqrt(2))^2sin^2(x)-1}}}=>{{{(sqrt(2)sin(x))^2-1}}}=>{{{(sqrt(2)sin(x)-1)(sqrt(2)sin(x)+1)}}}



{{{(sqrt(2)sin(x)-1)(sqrt(2)sin(x)+1)cos(x)=0}}}


solutions:

if {{{(sqrt(2)sin(x))-1=0}}} => {{{x=pi/4+2pi*n}}}, {{{x=3pi/4+2pi*n}}}

if {{{(sqrt(2)sin(x))+1=0}}}=>{{{x=5pi/4+2pi*n}}}, {{{x=7pi/4+2pi*n}}}

if {{{cos(x)=0}}} => {{{x=pi/2+2pi*n}}}, {{{x=3pi/2+2pi*n}}}

Combine all the solutions.