16sin^4 (11 п/2-2 а), если sin (3 п/2-4 а) = 1/4

16sin^4 (11π/2-2 а) = 16 * cos^4 (2α)

sin (3 п/2-4 а) = - cos (4 α) = - (cos ² (2α) - sin² (2α)) = sin² (2α) - cis² (2α) = 1-cos² (2α) - cos² (2α) = 1-2cos² (2 α) = 1/4

1-2cos² (2 α) = 1/4

-2cos² (2 α) = 1/4-1

cos² (2 α) = 3 / (4*2)

cos² (2 α) = 3/8

16 * cos^4 (2α) = 16 * cos² (2α) * cos² (2α) = 16 * 3/8 * 3/8 = 9/4 = 2,25

Ответ: 2,25