Question 963816
{{{(dy/dx)*tany = sin(x+y) +sin(x-y)}}}
{{{(dy/dx)*tany = 2sin(x)cos(y)}}}
{{{(sin(y)/cos^2(y))dy=2sin(x)dx}}}
Use a substitution,
{{{z=cos(y)}}}
{{{dz=-sin(y)*dy}}}
So then,
{{{-dz/z^2=2sin(x)dx}}}
{{{1/z=-2cos(x)+C}}}
{{{1/cos(y)=-2cos(x)+C}}}
{{{highlight(sec(y)=C-2cos(x))}}}