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Answer:
(7 -24√3)/50 = 0.14 -0.48√3
Explanation:
Sine is negative and cosine is positive in the 4th quadrant, so ...
sin(α) = -√(1 -cos(α)²) = -√(1 -576/625) = -7/25
Then the cosine of the angle sum is ...
cos(α +5π/6) = cos(α)cos(5π/6) -sin(α)sin(5π/6)
= (24/25)(-√3/2) -(-7/25)(1/2)
= (7 -24√3)/50 = 0.14 -0.48√3