Помогите с уравнием sin^4x+cos^4x=cos^2 2x+1/4

Question

leonid_fursov · Accepted Answer

Ответ. (sin(x))^4+(cos(x))^4=(cos(2*x))^2+1/4; (sin(x))^4+(cos(x))^4=((cos(x))^2-(sin(x))^2)^2+1/4; 0=-2*(cos(x))^2*(sin(x))^2+1/4;                    -0,5*(sin(2*x))^2+0,25=0; (sin(2*x))^2=0,5; sin(2*x1)=(0,5)^0,5; sin(2*x2)=-(0,5)^0,5;

diukhich · Answer

(sin^2(x) + cos^2(x))^2 - 2sin^2(x)cos^2(x) = cos^2(2x) + 1/4
1 - 0.5sin^2(2x) = 1 - sin^2(2x) + 1/4
0.5sin^2(2x) = 1/4
sin^2(2x) = 1/2
sin(2x) = -1/2
x1 = (-1)^(k+1) pi/12 + pik/2
sin(2x) = 1/2
x2 = (-1)^k pi/12 + pik/2, k E Z

larisa_kozina_32 · Answer

(1-cos^2(2x))\2+(1-cos^2(2x))\2=cos^2(2x)+1\4
cos^2(2x)=3\4
1) cos(2x)=-√3\2, 2x=+-5pi\6+2*pi*k, x=+-5*pi\12+pi*k
2) cos(2x)=√3\2, 2x=+-pi\6+2*pi*k, [=+-pi\12+pi*k