Question 114301
Step 1:  Remember that {{{csc(x)=1/sin(x)}}}


Step 2:  Substitute


{{{4*sin(x)=1/sin(x)}}}, then multiply both sides by {{{sin(x)}}}
{{{4*sin^2(x)=1}}}, then take the square root
{{{sqrt(4*sin^2(x))=+sqrt(1)}}} or {{{sqrt(4*sin^2(x))=-sqrt(1)}}}
{{{2*sin(x)=1}}} or {{{2*sin(x) = -1}}}
{{{sin(x)=1/2}}} or {{{sin(x)=-1/2}}}
{{{x=arcsin(1/2)}}} => {{{x=pi/6}}} or {{{x=5*pi/6}}}, or {{{x=arcsin(-1/2)}}} => {{{x=7*pi/6}}} or {{{x=11*pi/6}}}


Hope that helps,
John