( sinx-cosx)²+tgx=2sin²x
sinx²-2sinxcosx+cosx²+sinx/cosx=2sin²x
1-2sinxcosx+sinx/cosx=2sin²x
1+sinx/cosx=2sinxcosx+2sin²x
(cosx+sinx)/cosx=2sinx(cosx+sinx)
(cosx+sinx)(1/cosx-2sinx)=0
(cosx+sinx)((1-2sinxcosx)/cosx)=0
(cosx+sinx)((1-sin2x)/cosx)=0
1) cosx+sinx=0 :cosx; 1+tgx=0; tgx=-1; x=-π/4 +πn;
2) (1-sin2x)/cosx=0; т к cosx≠0; то 1-sin2x=0; sin2x=1; 2x=π/2 +2πn; x=π/4 +πn.
ответ: x=-π/4 +πn; x=π/4 +πn.