1) sin²x - 0,5sin2x=0;
sin²x - 0,5*2sinxcosx=0'
sinx(sinx - cosx)=0;
sinx = 0 ==>x= πk ;
sinx -cosx=0 ;
sinx=cosx ; (cosx≠ 0)
tqx = 1 ==> x= π/4 + πk;
2) 1 - cosx - 2sinx/2=0 ;
2sin²x/2 - 2sinx/2 = 0;
2sinx/2(sinx/2 - cosx/2) =0;
sinx/2=0 ==>x/2 = πk ==> x=2πk;
sinx/2 - cosx/2 = 0;
tqx/2=0 ;
x/2 = π/4 + πk ==> x= π/2+2πk ;
3) 1 + cos4x =cos2x ;
2cos²2x -cos2x=0 ;
2cos2x(cos2x - 1/2) =0;
cos2x=0 ==>2x = π/2+πk ==>x=π/4 + π/2*k ;
cos2x = 1/2 ==>2x =(+/-)π/3+2πk ==>x=(+/-)π/6 +πk .
Везде k целое число.