2sin²x-sin2x+sinx=cosx
2sin²x-2sinxcosx+sinx-cosx=0
2sinx(sinx-cosx)+(sinx-cosx)=0
(2sinx+1)(sinx-cosx)=0
1) 2sinx+1=0
2sinx=-1
sinx=-1/2
x=-π/6+2πn, n∈Z
x=-5π/6+2πn, n∈Z
2) sinx=cosx/:cosx≠0
sinx/cosx=1
tgx=1
x=π/4+πk, k∈Z
Ответ: x=-π/6+2πn, x=-5π/6+2πn, n∈Z; x=π/4+πk, k∈Z