Step-by-step explanation:
sin²(x) + cos²(x) = 1
cos²(x) = 1 - sin²(x)
cos(x/2) = ±sqrt((1 + cos(x))/2)
in our case
sin(x) = 1/4, tan(x) > 0, so cos(x) is positive too.
sin²(x) = 1/4² = 1/16
cos²(x) = 1 - 1/16 = 15/16
cos(x) = sqrt(15)/4
cos(x/2) = sqrt((1 + sqrt(15)/4)/2) = sqrt(1/2 + sqrt(15)/8) =
= sqrt(8/16 + 2×sqrt(15)/16) =
= 1/4 × sqrt(8 + 2×sqrt(15))
so, D is correct
