(300^1/2)*cos^2(19пи/12)-75^1/2

Compute the expression:

• sqrt(300) = 10√3, sqrt(75) = 5√3.
• So: sqrt(300) cos^2(19π/12) - sqrt(75) = 10√3 cos^2(19π/12) - 5√3
• Factor: = 5√3 [2 cos^2(19π/12) - 1] = 5√3 cos(2 · 19π/12) = 5√3 cos(19π/6)

Now cos(19π/6) = cos(3π + π/6) = -cos(π/6) = -√3/2.

Thus: 5√3 * (-√3/2) = -5 * 3 / 2 = -15/2.

Answer: -15/2.