16.а)2sinxcosx+sin²x=cosx
2sinxcosx+sin²x-cosx=0
sinx=t
2tcosx+t²-cosx=0
cosx(2t+t²-1)=0
cosx=0 2t+t²-1=0
x=π/2+πk t1=(-2-2√2)/2; t2=(-2+2√2)/2
sinx=(-2-2√2)/2-не сущ.
sinx=(-2+2√2)/2-не сущ.
б)x=π/2+πk
k=-1;x=π/2-π=-π/2
Ответ:а)x=π/2+πk
б)-π/2
17.а)cos2x+sinx=cos²x
cos²x-sin²x+sinx-cos²x=0
-sin²x+sinx=0
sinx(-sinx+1)=0
sinx=0 -sinx=-1; sinx=1
x=πk x=-π/2 +2πk
б)x=πk: x=-π/2 +2πk:
k=0; x=0 k=1; x=-π/2+2π=3π/2
k=1; x=π
k=2; x=2π
Ответ:а)x=πk;x=-π/2 +2πk
б)0;π;2π;3π/2