If sin theta = 1/4, theta in quadrant II, find the exact value of cos[theta + pi/6]

Using cos addition formula:

use x for theta

cos (x+π/6) = cosx*cos (π/6) - sinx*sin (π/6)

sinx=1/4

cosx=√15/4

cos (π/6) = √3/2

sin (π/6) = 1/2

cos (x+π/6) = (√15/4*√3/2) - (1/4*1/2)

cos (x+π/6) = (√45/8) - (1/8)

cos (x+π/6) = (√45-1) / 8)