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