Question 1178312

{{{2cos^2(x)-3=3sin(x)}}}

{{{2cos^2(x)=3sin(x)+3}}}

{{{cos(2 x) + 1=3sin(x)+3}}}

{{{cos(2 x) =3sin(x)+3-1}}}

{{{cos^2(x) - sin^2(x) =3sin(x)+2}}}............{{{cos^2(x)=1-sin^2(x) }}}

{{{1-sin^2(x)  - sin^2(x) =3sin(x)+2}}}

{{{1-2sin^2(x) =3sin(x)+2}}}

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

{{{2sin^2(x)+3sin(x)+1=0}}}

{{{2sin^2(x)+2sin(x)+sin(x)+1=0}}}

{{{(2sin^2(x)+sin(x))+(2sin(x)+1)=0}}}

{{{sin(x)(2sin(x)+1)+(2sin(x)+1)=0}}}

{{{(sin(x)+1)(2sin(x)+1)=0}}}

solutions:

if {{{(sin(x)+1)=0}}}=>{{{sin(x)=-1}}}
then

{{{x=sin^-1(-1)}}}

{{{x= -pi/2}}} ....periodicity of sin is {{{2pi}}}

{{{x= 2pi-pi/2}}}

{{{x= 3pi/2+2pi*n}}}

in interval [{{{0}}},{{{2pi}}})

{{{x= 270}}}°


if {{{2sin(x)+1=0}}}->{{{sin(x)=-1/2 }}}

{{{x=sin^-1(-1/2)}}}

{{{x=-pi/6}}}

{{{x=2pi-pi/6}}}

{{{x=11pi/6+2pi*n}}}

{{{x= 7pi/6+2pi*n}}}

in interval [{{{0}}},{{{2pi}}})

{{{ x= 210}}}° 

{{{x= 330}}}°