Question

2(sinx+cosx)+1+sin2x=0

Answer 1

$2(sinx+cosx)+1+sin2x=0$
$2(sinx+cosx)+sin^2x+cos^2x+2sinx*cosx=0$
$2(sinx+cosx)+(sinx+cosx)^2=0$
$(sinx+cosx)(sinx+cosx+2)=0$

$left[begin{array}{ccc}sinx+cosx=0\sinx+cosx=-2end{array}right= textgreater left[begin{array}{ccc}tgx=-1\sinx+cosx neq -2end{array}right= textgreater tgx=-1= textgreater$
$= textgreater x=-frac{pi}4+pi n;nin Z$