Question 1204390


 {{{cos(4x) - 3sin (3pi/2+ 2x) + 2 = 0}}}

using trigonometric identities to simplify

{{{cos^4(x) - 6 sin^2(x) cos^2(x) + sin^4(x)-3(-cos(2 x))+2=0}}}

{{{cos^4(x) - 6sin^2(x) cos^2(x) + sin^4(x)-3(1 - 2cos^2(x))+2=0}}}

{{{(cos^4(x)+ sin^4(x)) - 6sin^2(x) cos^2(x) -3 + 6cos^2(x)+2=0}}}

{{{(1 - 2cos^2(x) + 2cos^4(x))+ (6cos^2(x) - 6sin^2(x)*cos^2(x)) -1=0}}}

{{{1 - 2cos^2(x) + 2cos^4(x)+ 6cos^2(x)(1 - sin^2(x)) -1=0}}}}

{{{1 - 2cos^2(x) + 2 cos^4(x)+ 6cos^2(x)*cos^2(x) -1=0}}}

{{{ - 2 cos^2(x) + 2 cos^4(x)+ 6cos^4(x) =0}}}

 {{{8cos^4(x)- 2 cos^2(x)  =0}}}

{{{2cos^2(x) (4cos^2(x)- 1) =0}}}


solutions:

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

if {{{(4cos^2(x)- 1) =0 }}}=> {{{x = pi*n - pi/3}}}, {{{n}}} element {{{Z}}} , and {{{x = pi*n +pi/3}}}, {{{n}}} element {{{Z}}}

combine solutions:

{{{x =pi*n + pi/2}}}

{{{x = pi*n - pi/3}}}

{{{x = pi*n +pi/3}}}