Cos6x+sin^2 3x+2cos3x=0

Question

Cos6x+sin^2 3x+2cos3x=0

Answer 1

Так как cos 6x = cos( 2*3x) = cos^2 (3x) - sin^2 (3x);
cos 6x  + sin^2 (3x) + 2 cos(3x) = 0;
cos^2(3x) - sin^2(3x) + sin^2(3x) + 2 cos(3x) = 0;
cos^2(3x) + 2 cos(3x) = 0;
cos(3x)*(cos(3x) + 2) = 0;
1) cos 3x = 0;
3x = pi/2  + pi*k; ;
x = pi/6 + pi*k/3; k - Z.
2) cos(3x) + 2 = 0;
cos(3x) = -2 < -1; нет решений.
 Ответ x = pi/6 + pi*k/3; k-Z