Sinx(2sin^2(x)-1)+cos^2(2x)=0; [-1,6; 0,8]

-sinx(1-2sin²x)+(1-2sin²x)²=0(1-2sin²x)(-sinx+1-2sin²x)=0cos2x*(2sin²x+sinx-1)=0cos2x=0⇒2x=π/2+πn,n∈z⇒x=π/4+πn/2,n∈zn=-1⇒x=-π/2+π/4=-π/4∈[-1,6;0,8]n=0⇒x=π/4∈[-1,6;08]2sin²x+sinx-1=0sinx=a2a²+a-1=0D=1+8=9a1=(-1-3)/4=-1⇒sinx=-π/2+2πk,k∈zk=0⇒x=-π/2∈[-1,6;0,8]a2=(-1+3)/4=1/2⇒sinx=1/2x=π/6+2πm,m∈zm=0⇒x=π/6∈[-1,6;0,8]x=5π/6+2πc,c∈zнет корней на данном промежуткеx={-π/2;-π/4;π/4}