Question

(1+cos4x)sin2x=cos^2(2x)

Answer 1

(1+cos4x)*sin2x=cos^2(2x)

1+ cos4x = cos²2x + sin²2x + cos²2x - sin²2x = 2 cos²2x

Имеем: 2 cos²2x * sin2x = cos²2x

sin2x = cos²2x / 2cos²2x

sin2x = 1/2

2x = (-1)^n arcsin 1/2 + pi n,   n e Z

2x = (-1)^n pi/6 + pi n,     n e Z

x = (-1)^n pi/12 + (pi n)/2,     n e Z