2sinxcosx+√2sinx=2cosx+√2
sinx(2cosx+√2)-(2cosx+√2)=0
(2cosx+√2)(sinx-1)=0
2cosx+√2=0
cosx=-√2/2
x=-3π/4+2πk U x=3π/4+2πk,k∈x
sinx-1=0
sinx=1
x=π/2+2πk,k∈z
π≤-3π/4+2πk≤5π/2
4≤-3+8k≤10
7≤8k≤13
7/8≤k≤13/8
k=1 x=-3π/4+2π=5π/4
π≤3π/4+2πk≤5π/2
4≤3+8k≤10
1≤8k≤7
1/8≤k≤7/8
нет решения
π≤π/2+2πk≤5π/2
2≤1+4k≤5
1≤4k≤4
1/4≤k≤1
k=1 x=π/2+2π=5π/2