1. cos(π/6 + α) - sqrt(3)/2 * cos α = cos π/6 * cos α - sin π/6 * sin α - sqrt(3)/2 * cos α = sqrt(3)/2 * cos α - 1/2 * sin α - sqrt(3)/2 * cos α = -sin α / 2
2. sin 69 * cos 21 + cos 69 * sin 21 = sin (69 + 21) = sin 90 = 1
3. cos t = -sqrt(1 - sin^2 t) = -sqrt(1 - (4/5)^2) = -3/5
cos (π/6 + t) = cos π/6 * cos t - sin π/6 * sin t = sqrt(3)/2 * (-3/5) - 1/2 * 4/5 = -(3 sqrt(3) + 4)/10